A Comparison Process for Mouse Pairs

by John R. Steel

Overview

This book proves some important new theorems in the theory of canonical inner models for large cardinal hypotheses, a topic of central importance in modern set theory. In particular, the author 'completes' the theory of Fine Structure and Iteration Trees (FSIT) by proving a comparison theorem for mouse pairs parallel to the FSIT comparison theorem for pure extender mice, and then using the underlying comparison process to develop a fine structure theory for strategy mice. Great effort has been taken to make the book accessible to non-experts so that it may also serve as an introduction to the higher reaches of inner model theory. It contains a good deal of background material, some of it unpublished folklore, and includes many references to the literature to guide further reading. An introductory essay serves to place the new results in their broader context. This is a landmark work in inner model theory that should be in every set theorist's library.

Product Details

ISBN-13:	9781108840682
Publisher:	Cambridge University Press
Publication date:	11/24/2022
Series:	Lecture Notes in Logic , #51
Pages:	548
Product dimensions:	6.18(w) x 9.25(h) x 1.46(d)

About the Author

John R. Steel is Professor of Mathematics at the University of California, Berkeley. He is a recipient of the Carol Karp Prize of the Association for Symbolic Logic, the Hausdorff Medal of the European Set Theory Society, and the Humboldt Prize.

Table of Contents

1. Introduction; 2. Preliminaries; 3. Background-induced iteration strategies; 4. More mice and iteration trees; 5. Some properties of induced strategies; 6. Normalizing stacks of iteration trees; 7. Strategies that condense and normalize well; 8. Comparing iteration strategies; 9. Fine structure for the least branch hierarchy; 10. Phalanx iteration into a construction; 11. HOD in the derived model of a HOD mouse; References; Index.