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Universal models and definability

Published online by Cambridge University Press:  19 October 2011

OLIVIA CARAMELLO
OLIVIA CARAMELLO*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB. e-mail: O.Caramello@dpmms.cam.ac.uk
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Abstract

We establish some general results on universal models in Topos Theory and show that the investigation of such models can shed light on problems of definability in Logic as well as on De Morgan's law and the law of excluded middle for Grothendieck toposes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 2 , March 2012 , pp. 279 - 302
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

REFERENCES

[1]Ballard, D. and Boshuck, W.Definability and descent. J. Symbolic Logic 63 (1998), 372–378.CrossRefGoogle Scholar
[2]Blass, A. R.Functions on universal algebras. J. Pure Appl. Alg. 42 (1986), 25–28.CrossRefGoogle Scholar
[3]Butz, C. and Moerdijk, I.An elementary definability theorem for first order logic. J. Symbolic Logic 64 (1999), 1028–1036.CrossRefGoogle Scholar
[4]Caramello, O.De Morgan classifying toposes. Adv. Math. 222 (2009), 2117–2144.CrossRefGoogle Scholar
[5]Caramello, O. and Johnstone, P. T.De Morgan's law and the theory of fields. Adv. Math. 222 (2009), 2145–2152.CrossRefGoogle Scholar
[6]Caramello, O. Atomic toposes and countable categoricity, arXiv:math.CT/0811.3547 (2008), to appear in Applied Categorical Structures.Google Scholar
[7]Caramello, O. Lattices of theories (2009), arXiv:math.CT/0905.0299.Google Scholar
[8]Caramello, O. One topos, many sites (2009), arXiv:math.CT/0907.2361v1.Google Scholar
[9]Caramello, O. The unification of Mathematics via Topos Theory (2010), arXiv:math.CT/1006.3930v1.Google Scholar
[10]Johnstone, P. T. Factorization theorems for geometric morphisms, II. In Categorical aspects of topology and analysis, Lecture Notes in Math. 915 (Springer-Verlag, 1982).Google Scholar
[11]Johnstone, P. T. Sketches of an Elephant: a topos theory compendium. Vol. 1, Oxford Logic Guides 43 (Oxford University Press, 2002).Google Scholar
[12]Johnstone, P. T. Sketches of an Elephant: a topos theory compendium. Vol. 2, Oxford Logic Guides 44 (Oxford University Press, 2002).Google Scholar
[13]Mac Lane, S. and Moerdijk, I.Sheaves in Geometry and Logic: a First Introduction to Topos Theory (Springer-Verlag, 1992).Google Scholar
[14]Makkai, M.Strong conceptual completeness for first order logic. Ann Pure Appl. Logic 40 (1988), 167–215.CrossRefGoogle Scholar
[15]Makkai, M.Duality and definability in first order logic. Mem. Amer. Math. Soc. 503 (1993).Google Scholar
[16]Makkai, M. and Reyes, G. E.First order categorical logic. Lecture Notes in Math. 611 (Springer-Verlag, 1977).CrossRefGoogle Scholar
[17]Zawadowski, M. W.Descent and duality. Ann. Pure Appl. Logic 71 (1995), 131–188.CrossRefGoogle Scholar