"Ultracategories" by Lurie

Dear all, people on this list may be interested in the following new paper by Jacob Lurie: http://www.math.harvard.edu/~lurie/papers/Conceptual.pdf An extract: "In [9], Makkai proved a stronger form of Gödel’s completeness theorem, which provides a complete recipe for reconstructing the syntax of a first-order theory T (up to an appropriate notion of equivalence) from its semantics. The goal of this paper is to give a new proof of Makkai’s theorem and a reasonably self-contained exposition of the mathematics that surrounds it." Regards, David David Roberts http://ncatlab.org/nlab/show/David+Roberts http://thehighergeometer.wordpress.com/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]