Existentially closed models and locally zero-dimensional toposes

Mark Kamsma; Joshua Wrigley

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arXiv · 2406.02788

Existentially closed models and locally zero-dimensional toposes

Mark Kamsma·Joshua Wrigley

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Abstract

The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models extend to existentially closed geometric morphisms, such as the fact that every model admits a homomorphism to an existentially closed one. Other properties do not generalise: classically, there are two equivalent definitions of an existentially closed model, but this equivalence breaks down for the generalised notion. We study the interaction of these two conditions on the topos-theoretic level, and characterise the classifying topos of the e.c. geometric morphisms when the conditions coincide.

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BibTeX RIS

Mark Kamsma, Joshua Wrigley. 2024-06-04. Existentially closed models and locally zero-dimensional toposes. https://arxiv.org/abs/2406.02788

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