April 2006 - Categories - categories.org.au

Foundations?
by F W Lawvere 03 Sep '10

03 Sep '10

Down with "Foundations"! Up with algebra! Dear Friends, Presumably I am among those who are being "vilified" as "lovers of categories as foundation". By avoiding any precise definition, such a formulation might appeal to the widespread justified boredom induced by the past hundred years of "foundations as justification". Whenever I used the word "foundation" in my writings over the past forty years, I have explicitly rejected that reactionary use of the term and instead used the definition implicit in the work of my teachers Truesdell and Eilenberg. Namely, an important component of mathematical practice is the careful study of historical and contemporary analysis, geometry, etc. to extract the essential recurring concepts and constructions; making those concepts and constructions (such as homomorphism, functional, adjoint functor, etc.) explicit provides powerful guidance for further unified development of all mathematical subjects, old and new. What is the primary tool for such summing up of the essence of ongoing mathematics? Algebra! Nodal points in the progress of this kind of research occur when, as is the case with the finite number of axioms for the metacategory of categories, all that we know so far can be expressed in a single sort of algebra. I am proud to have participated with Eilenberg, Mac Lane, Freyd, and many others, in bringing about the contemporary awareness of Algebra as Category Theory Had it not been for the century of excessive attention given to the alleged possibility that mathematics is inconsistent, with the accompanying degradation of the F-word, we would still be using it in the sense known to the general public: the search for what is "basic". We, who supposedly know the explicit algebra of homomorphisms, functionals, etc. are long remiss in our duty to find ways to utilize those concepts also in guiding high school calculus. Best wishes, Bill Bibliography: - The Category of Categories as a Foundation for Mathematics, La Jolla conference 1965, Springer (1966) - Adjointness in Foundations, Dialectica, (1969), to be reprinted in TAC - Foundations and Applications: Axiomatization and Education, Bulletin of Symbolic Logic, (2003) vol 9, pp 213-224 - Sets for Mathematics, w/ Bob Rosebrugh, Cambridge Univ. Press, (2003) ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************

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dualities
by Peter Freyd 04 May '06

04 May '06

On the subject of favorite dualities: Surely the most important are the self-dualities and the most important of these (so important we stop noticing it as we age) is the category of finite-dimensional vector spaces over a given field. Next is Pontryagin's: the category of locally compact groups. The original Pontryagin duality easily generalizes: the category of locally compact modules over a given commutative ring is self-dual. (In the non-commutative case one also obtains a duality but not a self-duality -- unless, of course, the ring is self-dual.) A corollary is that the category of discrete left R-modules is dual to the category of compact right R-modules. (For 50 years I've been trying to turn this into an exercise in abelian categories. There's a nice reduction down to the proposition that R/Z is a cogenerator for the category of compact abelian groups, but that fact seems to require some non-trivial functional analysis.) Strange that two of the most important "dualities" are both Pontryagin's. The other is in algebraic topology theory. Then, of course there's my present favorite: the category of finitely presented group-valued functors from the category of finitely presented modules over a commutative ring.

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Does duality categorify?
by Vaughan Pratt 01 May '06

01 May '06

Does duality categorify? If so, how? If not, why not? For example distributive lattices categorify to distributive algebras. The dual of a distributive lattice is a partially ordered Stone space. What does categorification do here? (Apologies if this is an old chestnut.) Vaughan Pratt

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gr-stacks in the literature
by David Roberts 01 May '06

01 May '06

Dear all, after a bit of searching, I cannot find much in the literature about gr- stacks, more specifically, charts and presentations thereof reflecting (in a non-technical sense) the group-like structure. Also, aside from self equivalences of gerbes and quotients of groups (G/H for non-normal H), I cannot dream up other "interesting" examples - and these are the opposite ends of the spectrum I want to consider. All pointers welcome. -- David Roberts Pure Mathematics University of Adelaide South Australia, 5005

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Re: Products in a compact closed category
by Robin Houston 28 Apr '06

28 Apr '06

On Thu, Mar 23, 2006 at 12:17:05PM +0000, Robin Houston wrote: > I recently proved that [finite] products (or coproducts) in a compact > closed category are necessarily biproducts, and I'm wondering whether > this is a known theorem. Since a couple of you have been asking about this, I thought I should post a quick followup message. I had several private replies, almost all of them asking to see the proof. None of my respondents knew of an existing proof. A preliminary paper, describing the proof, in far more detail than most of the people on this list would need, is available from http://www.arxiv.org/abs/math.CT/0604542 (If any of you have any comments on it, I'd be interested in hearing them.) Yours, Robin

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MFPS 22 Program online
by Michael Mislove 26 Apr '06

26 Apr '06

Dear Colleagues, The Program for the Twenty-second Conference on the Mathematical Foundations of Programming Semantics is now available online. It can be found on the MFPS 22 web page, http://www.math.tulane.edu/~mfps/ mfps22.htm Information about registration and accommodation for the meeting is also available on that site. It should be noted that the Astor hHotel in Nervi that will house conference participants has extended the deadline for obtaining the conference rate. If you register this week, the conference rate will be honored. Best regards, Mike Mislove Co-Oranizer MFPS =============================================== Professor Michael Mislove Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University URL: http://www.math.tulane.edu/~mwm New Orleans, LA 70118 USA ===============================================

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ESSLLI 2006: Call for participation
by Ernesto Pimentel 24 Apr '06

24 Apr '06

ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 CALL FOR PARTICIPATION 18TH EUROPEAN SUMMER SCHOOL OF LOGIC, LANGUAGE AND INFORMATION July 31 - August 11, 2006 Malaga, Spain (Extended Early registration deadline: May 14, 2006) ESSLLI 2006 is organized by the Software Engineering Group of the University of Malaga, under the auspices of FoLLI, the European Association for Logic, Language and Information. The main focus of ESSLLI is on the interface between linguistics, logic and computation. The school has developed into an important meeting place and forum for discussion for students, researchers and IT professionals interested in the interdisciplinary study of Logic, Language and Information. The 18th edition of ESSLLI is offering 48 courses, organized into three interdisciplinary areas (Language & Computation, Language & Logic, and Logic & Computation), at a variety of levels (foundational, introductory, advanced), as well as seven workshops. All the information may be found at: http://esslli2006.lcc.uma.es Foundational courses aim to provide truly introductory courses into a field. The courses presuppose absolutely no background knowledge. In particular, they should be accessible to people from other disciplines. Introductory courses are intended to equip students and young researchers with a good understanding of a field's basic methods and techniques, and to allow experienced researchers from other fields to acquire the key competences of neighboring disciplines, thus encouraging the development of a truly interdisciplinary research community. Advanced courses are intended to enable participants to acquire more specialized knowledge about topics they are already familiar with. Workshops are intended to encourage collaboration and the cross-fertilization of ideas by stimulating in-depth discussion of issues which are at the forefront of current research in the field. In these workshops, students and researchers can give presentations of their research. In addition to courses and workshops a student session is being also organized, with the aim of providing Masters and PhD students with an opportunity to present their own work to a professional audience, thereby getting informed feedback on their own results. Unlike workshops, the student session is not tied to any specific theme. If you are interested in presenting a paper to any of the ESSLLI workshops, you can access to their call for papers through the following link http://esslli2006.lcc.uma.es. The early (extended) registration deadline is May 14, 2006. Ernesto Pimentel Local Organizing Committee Chair University of Malaga esslli2006(a)lcc.uma.es ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006 ESSLLI 2006

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algebra and coalgebra: positions for 3 PhDs and 1 postdoc
by Yde Venema 24 Apr '06

24 Apr '06

----------------------------------------------------- ALGEBRA & COALGEBRA: POSITIONS FOR 3 PhDs & 1 POSTDOC ----------------------------------------------------- As of September 2006, funding for 3 PhD studants and 1 postdoc will be available at the Universiteit van Amsterdam in the area of Logic and Theoretical Computer Science. The appointees will join the NWO sponsored research project ALGEBRA AND COALGEBRA (the mathematical environments of modal logic) which is funded by the Dutch research organisation NWO and directed by Dr. Yde Venema. Successful candidates will be working at the Institute for Logic, Language and Computation. The PhD students will concentrate on one of the following projects: Modal fixpoint logic Partially ordered algebra Universal coalgebra The post-doc will perform research preferably in the following area: Coalgebra automata. More information on the positions is available on http://www.uva.nl/vacatures/object.cfm/objectid=A44F58E5-560B-489C-B1DCE785… or via the web page of Dr. Venema: http://staff.science.uva.nl/~yde ------------------------------------------------------------------------------

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SOS 2006 - Call for Papers
by SOS 2006 Organisers 24 Apr '06

24 Apr '06

Second Call for Papers: Structural Operational Semantics 2006 A Satellite Workshop of CONCUR 2006 August 26, 2006, Bonn, Germany http://www.cse.unsw.edu.au/~rvg/SOS2006 Aim: Structural operational semantics (SOS) provides a framework for giving operational semantics to programming and specification languages. A growing number of programming languages from commercial and academic spheres have been given usable semantic descriptions by means of structural operational semantics. Because of its intuitive appeal and flexibility, structural operational semantics has found considerable application in the study of the semantics of concurrent processes. Moreover, it is becoming a viable alternative to denotational semantics in the static analysis of programs, and in proving compiler correctness. Recently, structural operational semantics has been successfully applied as a formal tool to establish results that hold for classes of process description languages. This has allowed for the generalisation of well-known results in the field of process algebra, and for the development of a meta-theory for process calculi based on the realization that many of the results in this field only depend upon general semantic properties of language constructs. This workshop aims at being a forum for researchers, students and practitioners interested in new developments, and directions for future investigation, in the field of structural operational semantics. One of the specific goals of the workshop is to establish synergies between the concurrency and programming language communities working on the theory and practice of SOS. Moreover, it aims at widening the knowledge of SOS among postgraduate students and young researchers worldwide. Specific topics of interest include (but are not limited to): * programming languages * process algebras * higher-order formalisms * rule formats for operational specifications * meaning of operational specifications * comparisons between denotational, axiomatic and SOS * compositionality of modal logics with respect to operational specifications * congruence with respect to behavioural equivalences * conservative extensions * derivation of proof rules from operational specifications * software tools that automate, or are based on, SOS. Papers reporting on applications of SOS to software engineering and other areas of computer science are welcome. History: The first SOS Workshop took place in August 2004 in London as one of the satellite workshops of CONCUR 2004, and was attended by over 30 participants [http://www.cs.aau.dk/~luca/SOS-WORKSHOP/] The second SOS Workshop occurred in July 2005 in Lisbon as a satellite workshop of ICALP 2005, and attracted 19 submissions [http://www.cs.le.ac.uk/events/SOS2005/] INVITED SPEAKERS: * Robin Milner (Cambridge, UK; joint invited speaker with EXPRESS 2006) * Bartek Klin (Sussex, UK) PAPER SUBMISSION: We solicit unpublished papers reporting on original research on the general theme of SOS. Prospective authors should register their intention to submit a paper by uploading a title and abstract via the workshop web page by: *** Friday 26 May 2006. *** Papers should take the form of a dvi, postscript or pdf file in ENTCS format [http://www.entcs.org/] whose length should not exceed 15 pages (not including an optional "Appendix for referees" containing proofs that will not be included in the final paper). We will also consider 5-page papers describing tools to be demonstrated at the workshop. Submissions from PC members are allowed. Proceedings: Preliminary proceedings will be available at the meeting. The final proceedings of the workshop will appear as a volume in the ENTCS series. If the quality and quantity of the submissions warrant it, the co-chairs plan to arrange a special issue of an archival journal devoted to full versions of selected papers from the workshop. IMPORTANT DATES: * Submission of abstract: Friday 26 May 2006 * Submission: Sunday 4 June 2006, midnight GMT * Notification: Wednesday 28 June 2006 * Final version: Friday 14 July 2006 * Workshop: Saturday 26 August 2006 * Final ENTCS version: Friday 29 September 2006. PROGRAMME COMMITTEE Rocco De Nicola (Florence, IT) Wan Fokkink (Amsterdam, NL) Rob van Glabbeek (NICTA, AU, co-chair) Reiko Heckel (Leicester, UK) Matthew Hennessy (Sussex, UK) Ugo Montanari (Pisa, IT) Peter Mosses (Swansea, UK, co-chair) MohammadReza Mousavi (Eindhoven, NL) David Sands (Chalmers, SE) Irek Ulidowski (Leicester, UK) Shoji Yuen (Nagoya, JP) CONTACT: sos2006(a)cs.stanford.edu WORKSHOP ORGANISERS: Rob van Glabbeek National ICT Australia Locked Bag 6016 University of New South Wales Sydney, NSW 1466 Australia Peter D. Mosses Department of Computer Science Swansea University Singleton Park Swansea SA2 8PP United Kingdom

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Computability in Europe 2006 - Call for Participation
by A.Beckmann＠swansea.ac.uk 21 Apr '06

21 Apr '06

[Apologies for multiple copies] CiE 2006 Computability in Europe 2006 : Logical Approaches to Computational Barriers 30 June - 5 July 2006 Swansea University, United Kingdom http://www.cs.swansea.ac.uk/cie06/ cie06(a)swansea.ac.uk CALL FOR PARTICIPATION Important deadlines: Informal Presentations 30 April, 2006 Early registration 15 May, 2006 * Some grants for UK students are still available * CiE 2006 is the second of a new conference series which serves as an interdisciplinary forum for researchers into all aspects of computability and the foundations of computer science. The scientific programme consists of two three-hour tutorials, nine plenary talks, six special sessions with four talks each, and over sixty contributed talks. For more details on the programme see the full list of talks below, or visit http://www.cs.swansea.ac.uk/cie06/ The conference venue and accommodation will be on the campus of Swansea University. Swansea lies at the southcoast of Wales, next to the beautiful Gower Peninsula. To register, submit an informal presentations, apply for a UK student grant, or to obtain any other information visit http://www.cs.swansea.ac.uk/cie06/ Contact: cie06(a)swansea.ac.uk ********* PROGRAMME ********* TUTORIALS Samuel R. Buss (San Diego, CA) Proof Complexity and computational hardness Julia Kempe (Paris) Quantum Algorithms PLENARY TALKS Jan Bergstra (Amsterdam) Elementary Algebraic Specifications of the Rational Function Field Luca Cardelli (Microsoft Research) Biological systems as reactive systems Martin Davis (New York, NY) The Church-Turing thesis: consensus and opposition John W Dawson (York, PA) Goedel and the origins of computer science Jan Krajicek (Prague) Forcing with random variables and proof complexity Elvira Mayordomo Camara (Zaragoza) The fractal dimension of complexity classes Istvan Nemeti (Budapest) Can general relativistic computers break the Turing barrier? Helmut Schwichtenberg (Munich) Program extraction from proofs in constructive analysis Andreas Weiermann (Utrecht) Phase transition thresholds in recursion theory SPECIAL SESSIONS PROOFS AND COMPUTATION organised by Alessandra Carbone and Thomas Strahm Kai Bruennler (Bern) Deep inference Roy Dyckhoff (St Andrews) LJQ: a focused calculus for intuitionistic logic Thomas Ehrhard (Marseille) About the Krivine machine and the Taylor expansion of lambda-terms Georges Gonthier (Microsoft Research) Using reflection to prove the Four Colour Theorem COMPUTABLE ANALYSIS organised by Peter Hertling and Dirk Pattinson Margarita Korovina (Aarhus) Complexity of bisimulations on Pfaffian hybrid systems Paulo Oliva (London) Computational interpretations of proofs in classical analysis Matthias Schroeder (Edinburgh) Admissible representations in computable analysis Xizhong Zheng (Cottbus) Computability theory of real numbers CHALLENGES IN COMPLEXITY organised by Klaus Meer and Jacobo Toran Johannes Koebler (Berlin) Complexity of graph isomorphism for restricted graph classes Sophie Laplante (Paris) Lower bounds using Kolmogorov complexity Janos A. Makowsky (Haifa) Computable graph invariants Mihai Prunescu (Freiburg) The fast elimination of quantifiers and some structures with P=NP according to the unit-cost model of computation FOUNDATIONS OF PROGRAMMING organised by Inge Bethke and Martin Escardo Erika Abraham (Freiburg) Fully abstract semantics of concurrent class-based languages Roland Backhouse (Nottingham) Datatype-Generic Reasoning James Leifer (INRIA, Le Chesnay) Transactional atomicity in programming languages Alban Ponse (Amsterdam) Program and thread algebra MATHEMATICAL MODELS OF COMPUTERS AND HYPERCOMPUTERS organised by Joel D Hamkins and Martin Ziegler Jean-Charles Delvenne (Louvain-la-Neuve) Turing-universal dynamical systems Benedikt Loewe (Amsterdam) Infinite time complexity theory Klaus Meer (Odense) Optimization and approximation problems related to polynomial system solving Philip Welch (Bristol) Admissibility and infinite time computation GOEDEL CENTENARY: HIS LEGACY FOR COMPUTABILITY organised by Matthias Baaz and John W Dawson Arnon Avron (Tel Aviv) From constructibility and absoluteness to computability and safety Torkel Franzen (Lulea) What does the incompleteness theorem add to the unsolvability of the halting problem? Wilfried Sieg (Pittsburgh, PA) Goedel's Conflicting approaches to effective calculability Richard Zach (Calgary, AB) Kurt Goedel, logic, and theoretical computer science CONTRIBUTED TALKS Hajnal Andreka (Budapest) Relativity theory for logicians and new computing paradigms Marat Arslanov (Kazan) Generalized tabular reducibilities in infinite levels of Ershov hierarchy Josef Berger (Munich) The logical strength of the uniform continuity theorem Jens Blanck (Swansea) Note on Reducibility Between Domain Representations Paul Brodhead, Douglas Cenzer and Seyyed Dashti (Florida) Random Closed Sets Riccardo Bruni (Florence) Goedel, Turing, the Undecidability Results and the Nature of Human Mind Douglas Cenzer (Florida) and Zia Uddin (Lock Haven, PA) Logspace Complexity of Functions and Structures Alexey Chernov (Manno) and Juergen Schmidhuber (Munich) Prefix-like Complexities and Computability in the Limit Jose Felix Costa (Lisbon) and Jerzy Mycka (Lublin) The conjecture P =/= NP given by some analytic condition Paolo Cotogno (Brescia) Decidability of arithmetic through hypercomputation: a logical objection Fredrik Dahlgren (Uppsala) Partial Continuous Functions and Admissible Domain Representations Ugo Dal Lago and Simona Martini (Bologna) An Invariant Cost Model for the Lambda Calculus Stefan Dantchev (Durham) On the complexity of the Sperner Lemma Gregorio de Miguel Casado and Juan Manuel Garcia Chamizo (Alicante) The Role of Algebraic Models and TTE in Special Purpose Processor Design Paulin Jacobe de Naurois (Paris) A Measure of Space for Computing over the Reals Pavel Demenkov (Novosibirsk) Computer simulation replacements aminoacids in proteins David Doty (Iowa) Every Sequence is Decompressible from a Random One Jerome Durand-Lose (Orleans) Reversible conservative rational abstract geometrical computation is Turing-universal Birgit Elbl (Munich) On generalising predicate abstraction Willem Fouche (Pretoria) Brownian motion and Kolmogorov complexity Gassner Christine (Greifswald) A Structure with P = NP Alexander Gavryushkin (Novosibirsk) On Complexity of Ehrenfeucht Theories with Computable Model Annelies Gerber (Paris) Some mathematical properties of input resolution refutations with non-tautological resolvents Philipp Gerhardy (Darmstadt) Functional interpretation and modified realizability interpretation of the double-negation shift Guido Gherardi (Siena) An Analysis of the Lemmas of Urysohn and Urysohn-Tietze according to effective Borel measurability Lev Gordeev (Tuebingen) Toward combinatorial proof of P < NP. Basic approach Neal Harman (Swansea) Models of Timing Abstraction in Simultaneous Multithreaded and Multi-Core Processors Charles Milton Harris (Leeds) Enumeration reducibility with polynomial time bounds Eiju Hirowatari (Kitakyushu), Kouichi Hirata (Kyushu) and Tetsuhiro Miyahara (Hiroshima) Finite Prediction of Recursive Real-Valued Functions Tie Hou (Swansea) Coinductive Proofs for Basic Real Computation Iskander Kalimullin (Kazan, Russia) The Dyment reducibility on the algebraic structures and on the families of subsets of omega Dazhou Kang, Baowen Xu, Jianjiang Lu and Yanhui Li (Southeast University, China) Reasoning within the Extended Fuzzy Description Logics with Restricted Boxes Peter Koepke (Bonn) Infinite time register machines Peter Koepke (Bonn) and Ryan Siders (Helsinki) Computing the Recursive Truth Predicate on Ordinal Register Machines Ekaterina Komendantskaya and Anthony Seda (Cork) Bilattice-based Logic Programs: Automated Reasoning and Neural Computation Shankara Narayanan Krishna (Bombay) Upper and Lower Bounds for the Computational Power of P Systems with Mobile Membranes Lars Kristiansen (Oslo) Complexity-Theoretic Hierarchies Oleg Kudinov and Victor Selivanov (Novosibirsk) Undecidability in the Homomorphic Quasiorder of Finite Labeled Forests Andrew Edwin Marcus Lewis (Siena) The jump classes of minimal covers Chung-Chih Li (Beaumont, TX) Clocking Type-2 Computation in The Unit Cost Model John Longley (Edinburgh) On the calculating power of Laplace's demon Maria Lopez-Valdes (Zaragoza) Scaled Dimension of Individual Strings Barnaby Martin and Florent Madelaine (Durham) Towards a Trichotomy for Quantified H-Coloring Klaus Meer (Odense) and Martin Ziegler (Paderborn) Uncomputability below the Real Halting Problem Greg Michaelson (Edinburgh) and Paul Cockshott (Glasgow) Constraints on hypercomputation Philippe Moser (Maria de Luna) Martingale Families and Dimension in P Benedek Nagy and Sandor Valyi (Debrecen) Solving a PSPACE-complete problem by a linear interval-valued computation Keng Meng Ng (Wellington), Frank Stephan (Singapore) and Gouhua Wu (Singapore) Degrees of Weakly Compact Reals Peter Peshev and Dimiter Skordev (Sofia) A Subrecursive Refinement of the Fundamental Theorem of Algebra Petrus Hendrik Potgieter (Pretoria) Hypercomputing the Mandelbrot Set? Vadim Puzarenko (Novosibirsk) Definability of the Field of Reals in Admissible Sets Rose Hafsah Abdul Rauf (Swansea) Integrating Functional Programming Into C++: Implementation and Verification Mihai Prunesco (Bucharest/Freiburg) Fast quantifier elimination means P = NP Peter Schuster and Julia Zappe (Munich) Do Noetherian modules have Noetherian basis functions? Anton Setzer (Swansea) Partial Recursive Functions in Martin-Loef Type Theory Merlijn Sevenster (Amsterdam) and Tero Tulenheimo (Helsinki) Partially ordered connectives and Sigma-1-1 on finite models Alan Skelley (Prague) Third-Order Computation and Bounded Arithmetic Boris Solon (Ivanovo) Co-total enumeration degrees Ivan Soskov (Sofia) Extensions of the semi-lattice of the enumeration degrees Alexandra Soskova (Sofia) Relativized Degree Spectra Alexey Stukachev (Novosibirsk) On inner constructivizability of admissible sets Andreas Weiermann and Arnoud den Boer (Utrecht) A sharp phase transition threshold for elementary descent recursive functions Albert Ziegler (Munich) Some Reflections on the Principle of Image Collection Jeffery Zucker (McMaster) Primitive Recursive Selection Functions over Abstract Algebras PROGRAMME COMMITTEE Samson Abramsky (Oxford), Benedikt Loewe (Amsterdam), Klaus Ambos-Spies (Heidelberg), Yuri Matiyasevich (St. Petersburg), Arnold Beckmann (co-chair), Dag Normann (Oslo), Ulrich Berger (Swansea), Giovanni Sambin (Padova), Olivier Bournez (Nancy), Uwe Schoening (Ulm), Barry Cooper (Leeds), Andrea Sorbi (Siena), Laura Crosilla (Florence), Ivan Soskov (Sofia), Costas Dimitracopoulos (Athens), Leen Torenvliet (Amsterdam), Abbas Edalat (London), John Tucker (Swansea, co-chair), Fernando Ferreira (Lisbon), Peter van Emde Boas (Amsterdam), Ricard Gavalda (Barcelona), Klaus Weihrauch (Hagen), Giuseppe Longo (Paris) ORGANISERS Arnold Beckmann, Ulrich Berger, S Barry Cooper, Phil Grant, Oliver Kullmann, Benedikt Loewe, Faron Moller, Monika Seisenberger, Anton Setzer, John V Tucker CiE 2006 received financial support by the Department of Computer Science at Swansea, the British Logic Colloquium (BLC), the British Engineering and Physical Sciences Research Council (EPSRC), the Kurt Goedel Society (KGS) in Vienna, the London Mathematical Society (LMS), the Welsh Development Agency (WDA) and IT Wales. Other sponsors are the Association for Symbolic Logic (ASL), the British Computer Society (BCS) and the European Association for Theoretical Computer Science (EATCS).

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