Natural Models, Second-order Logic & Categoricity in Set Theory

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Natural Models, Second-order Logic & Categoricity in Set Theory

Type: Bachelor thesis
Title: Natural Models, Second-order Logic & Categoricity in Set Theory
Author: Hekking, Jeroen
Issue Date: 2015-12-31
Keywords: second-order logic
set theory
semi-categoricity
Henkin semantics
Abstract: Among philosophically relevant logical results Zermelo’s semi-categoricity theorem has received little to no attention. This is notwithstanding the fact that the present-day canonical foundation of mathematics, that is first-order Zermelo-Fraenkel set theory, fails horribly at unambiguous denotation. The aim of the present study is to offer a reasonably self-contained and modern presentation of Zermelo’s theorem that is accessible also to a philosopher with some knowledge of elementary set- and model theory. In a modern framework semi-categoricity cannot be interpreted as a result on first order models. Using full second-order models one salvages external, or ‘true’, semi-categoricity, although one then loses a sound and complete deductive calculus. With Henkin semantics one does have completeness, but retains only internal semi-categoricity.
Supervisor: Sundholm, Göran
Faculty: Faculty of Humanities
Department: Wijsbegeerte (Bachelor)
Specialisation: Theoretische filosofie
ECTS Credits: 10
Handle: http://hdl.handle.net/1887/37474
 

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