Logic Seminar

Liron CohenCornell University
A minimal predicative framework for formalizing mathematics

Tuesday, November 8, 2016 - 2:55pm
Malott 206

We describe a framework for formalizing mathematics which is based on the usual set theoretical foundations of mathematics. Its most important feature is that it reflects real mathematical practice as presented in ordinary mathematical discourse by making extensive use of abstract set terms. We show how large portions of scientifically applicable mathematics can be developed in this framework in a straightforward way, using just rather weak predicative systems and their corresponding minimal universes. The key property of those theories is that every object which is used in it is defined by some closed term of the theory. This allows for a very concrete, computationally-oriented interpretation.