Canonical powersets over canonical models

Profile

Dominik Adolf is a researcher at the Institute for Advanced Studies in Mathematics at the Harbin Institute of Technology. His research interests are mathematical logic, especially set theory, in particular inner model theory and the theory of stationary sets, specifically Chang’s Conjecture, Mutual Stationarity and their intersections. He has publications in first-rate journals including the Journal of American Mathematical Society.

Dominik Adolf is a researcher at the Institute for Advanced Study in Mathematics at Harbin Institute of Technology. His research interests lie in mathematical logic, particularly set theory, with a focus on inner model theory and stationary set theory, especially Chang's Conjecture, mutual stationarity, and their intersection. His papers have been published in top journals, including the Journal of the American Mathematical Society.

Abstract

Inner Model Theory going back to Gödel's constructible universe L concerns itself with the study of canonical models of set theory. In this talk we will discuss when the 'stack', a sort of canonical powerset, over a canonical model exists. We will show that this is always the case when the height of the structure has uncountable cofinality. These results, we believe, will be crucial to extending the theory of core models which in turn are essential to computing the consistency strength of extensions of the usual axioms of mathematics.