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...Show moreAmong 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.Show less
