Categorical semantics of modal doctrines.

Title: Categorical semantics of modal doctrines.
Identifier: AAI9530901
identifier: 9530901
Creator: Mannucci, Mirco Antonio.
Contributor: Adviser: Alex Heller
Date: 1995
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: We consider an elementary topos together with a lex endofunctor acting on it (a modal topos in our notation) and show that such a pair provides a universe appropriate for a semantics of first order modal theories. A comparison between this categorical structure and the classical Kripke frames is established. We also prove a representation theorem of modal doctrines and discuss the notion of classifying modal topos for a given modal geometric theory. Lastly, we introduce some generalisations of this approach to multimodal operators and investigate connections with other categorical approaches to modality.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.