London Logic Forum: Logic Day

UCL Contact: Robin Hirsch (Visitors from outside UCL please email in advance).
Date/Time: 28 Jun 16, 12:00 - 13:00
Venue: Roberts 309

Abstract

Programme

12:00. Tutorial on the elementary theory of ultraproducts and ultrapowers. We will start from the definition of a boolean algebra and get up to Los theorem and maybe something on game strategies over ultraproducts. These techniques, developed in the 1930s and 1950s, are useful for proving that a class of structures cannot be finitely axiomatised or for proving that a class is not determined by any first order theory. The material may be used in the seminars in the afternoon.

13:00 Lunch.

14:00 Rob Egrot. Axiomatising representation classes for posets in first order logic (abstract attached).

15:15 Robin Hirsch and Brett McLean. The first-order logic of disjoint union

Abstract: Disjoint union is a partial binary operation on sets, defined if and only if the two sets are disjoint, in which case it yields the union. This operation is used in the semantics of separation logic, where it is applied to abstract models of heap states. We will talk about the class of partial algebras representable as algebras of sets equipped with disjoint union. We will describe an infinite first-order axiomatisation of this representation and then show that no finite axiomatisation exists. We will also discuss a possible notion of complete representability.

16:30 Kikot, Kurucz, Tanaka, Wolter, Zakharyaschev. On the completeness of EL-equations: first results.