# Determinacy in analysis and beyond

## Philip Welch

### University of Bristol

Recently Montalban and Shore derived precise limits to the amount of determinacy provable in second order arithmetic. We review some of the results in this area and recent work on lifting this to a setting of ZF^- with a single measurable cardinal.

Professor Welch (Professor of Mathematical Logic, University of Bristol) conducts research on a broad selection of topics in mathematical and philosophical logic. In set theory, he is a leading researcher on the topics of fine structure and core models, problems concerning determinancy, large cardinals and strong axioms of infinity. He has worked in the philosophy of mathematics on the foundations of set theory and theories of truth. And he has been a central figure in the recently intensified work on infinitary models of computation.