Extremal Assumptions & Categoricity

Logic Café Lecture
The Philosophy Department and the Institute Vienna Circle are jointly organizing a series of talks this term

Date: 22/05/2023

Time: 16h45- 18h15

Meetings are usually held on Mondays from 16:45 to 18:15 in Raum 3F (D0313), 3. floor Department of Philosophy

Abstract:

Extremal axioms impose a condition of either minimality or maximality on the admissible models of an axiomatic theory. For example, while the axiom of Induction enforces the requirement of minimality on the models of Peano arithmetic, the axiom of Line Completeness imposes the condition of maximality over the models of Hilbert geometry. Similar extremal assumptions have been adopted in real analysis, non-standard analysis and set theory. The idea of extremal assumptions is potentially much more important than has been pointed out in the literature -- with the exceptions of Carnap & Bachmann (1936), Hintikka (1998) and Schiemer (2012). In this talk, I will address two main questions: (i) How to formulate extremal assumptions in a suitable logical language? (ii) Under what conditions do extremal assumptions entail the categoricity of the theory?