Ομιλητής: Ali Enayat, University of Gothenburg (Sweden)

Title: Leibnizian motifs in set theory

Ημερομηνία: Τετάρτη, 22/6/2016, 6-7 μ.μ.

Αίθουσα: Γ. Γκουνταρούλη (στο ισόγειο του κτηρίου γραφείων), Τμήμα ΜΙΘΕ (δίπλα στην κεντρική πύλη της Παν/πολης)

Leibniz's principle of identity of indiscernibles stipulates that no two distinct substances exactly resemble each other; a principle that can be construed as prescribing a logical relationship between objects and properties: any two distinct objects must differ in at least one property. In this talk I will describe how Leibniz's principle, surprisingly, connects to the metamathematics of set theory. As we shall see, a natural model-theoretic formulation of Leibniz's principle holds for finite set theory (Zermelo-Fraenkel set theory, ZF, with the axiom of infinity replaced by its negation), but in the case of general set theory (ZF), the principle is equivalent to a weak version of the global form of the axiom of choice that is consistent with ZF, but unprovable in ZF.