De Morgan's law in toposes I
Olivia Caramello, Yorgo Chamoun
TL;DR
This paper explores toposes satisfying De Morgan's law, providing characterizations of theories with De Morgan classifying toposes and methods to transform toposes into De Morgan toposes.
Contribution
It offers new characterizations of geometric theories with De Morgan classifying toposes and introduces methods to convert toposes into De Morgan toposes.
Findings
Characterizations of geometric theories with De Morgan classifying toposes
Links between De Morgan property and the amalgamation property
Methods to turn a topos into a De Morgan topos
Abstract
We study toposes satisfying De Morgan's law, in particular we give characterizations of geometric theories whose classifying topos is De Morgan, clarifying the link with the amalgamation property of the category of models of such theory. We then give several ways of turning a topos into a De Morgan topos.
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