Speaker: Laurenz Hudetz
Date and Time: Friday, February 10th 2017, 15:30-17:00
Venue: KdVI Seminar Room F3.20, Science Park 107.
Title: Remarks on formal criteria of theory equivalence.
Abstract. Philosophers of science have recently developed increased interest in formal criteria of theory equivalence (Andréka, Madarász and Németi 2008, Barrett and Halvorson 2016, Halvorson 2016, Weatherall 2016). The two most important criteria presently discussed are:
(1) generalised definitional equivalence (or generalised bi-interpretability),
(2) categorical equivalence (i.e. equivalence of categories of models).
After presenting these criteria and their motivations, I introduce a strengthening of categorical equivalence, called `definable categorical equivalence’, which takes into account the internal structure of models (in contrast to categorical equivalence). I illustrate the properties of this criterion by means of examples. Then I address questions about the relationships between these criteria, in particular:
(a) For which theories does definable categorical equivalence imply generalised bi-interpretability?
(b) For which theories does generalised bi-interpretability imply definitional equivalence?