# Reverse mathematics of non-deterministic inductive definitions

**Date**: Wednesday 14 November 2018, 16:15 – 17:15**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Logic, Seminars, Pure Mathematics**Cost**: Free

#### Hajime Ishihara, Japan Advanced Institute of Science and Technology. Part of the Logic Seminar Series.

We present some reverse mathematics within a constructive set theory and classify the following theorems in terms of non-deterministic inductive definition (NID) principles:

Fullness;

The category of basic pairs and relation pairs has coequalisers;

The category of sets and relations has weak coequalisers;

The category of concrete spaces and convergent relation pairs has equalisers;

The class of formal points of a set-presented formal topology is set-generated;

The class of models of a geometric theory is set-generated.

This is a joint work with Ayana Hirata, Tatsuji Kawai and Takako Nemoto.