Saturated models of intuitionistic theories

Annals of Pure and Applied Logic 129 (1-3):245-275 (2004)
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Abstract

We use the language of categorical logic to construct generic saturated models of intuitionistic theories. Our main technique is the thorough study of the filter construction on categories with finite limits, which is the completion of subobject lattices under filtered meets. When restricted to coherent or Heyting categories, classifying categories of intuitionistic first-order theories, the resulting categories are filtered meet coherent categories, coherent categories with complete subobject lattices such that both finite disjunctions and existential quantification distribute over filtered meets. Such categories naturally embed into Grothendieck toposes which then contain saturated models of the theory we started with

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Citations of this work

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References found in this work

A model for intuitionistic non-standard arithmetic.Ieke Moerdijk - 1995 - Annals of Pure and Applied Logic 73 (1):37-51.
Developments in constructive nonstandard analysis.Erik Palmgren - 1998 - Bulletin of Symbolic Logic 4 (3):233-272.
Minimal models of Heyting arithmetic.Ieke Moerdijk & Erik Palmgren - 1997 - Journal of Symbolic Logic 62 (4):1448-1460.
Minimal models of Heyting arithmetic.Ieke Moerdijk & Erik Palmgren - 1997 - Journal of Symbolic Logic 62 (4):1448-1460.

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