Of course not ! Elementary toposes are models of a first order theory (this is also true for elementary toposes with an NNO) . Thus there are countable models. In such a model the answer is no. Le 20 nov. 07 à 13:10, Lutz Schroeder a écrit :
Is the Heyting algebra of global elements of the classifier in an elementary topos always complete? (Of course, the classifier is complete internally; here, I mean externally complete.) I suspect not, but I can't presently think of a natural counterexample.
Thanks,
Lutz Schröder
-- ------------------------------------------------------------------ PD Dr. Lutz Schröder office @ Universität Bremen: Senior Researcher Cartesium 2.051 Safe and Secure Cognitive Systems Enrique-Schmidt-Str. 5 DFKI-Lab Bremen FB3 Mathematik - Informatik Robert-Hooke-Str. 5 Universität Bremen D-28359 Bremen P.O. Box 330 440 D-28334 Bremen phone: (+49) 421-218-64216 Fax: (+49) 421-218-9864216 mail: Lutz.Schroeder@dfki,de www.dfki.de/sks/staff/lschrode ------------------------------------------------------------------
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