A comparison process for mouse pairs 1st edition by John Steel 110884068X 978-1108840682
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ISBN-10 : 110884068X
ISBN-13 : 978-1108840682
Author : John R. Steel
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 It contains a good deal of background material, some of it unpublished folklore, and includes many references to the literature to guide further reading.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.
A comparison process for mouse pairs 1st Table of contents:
Chapter 1 – Introductionpp 1-18
Chapter 2 – Preliminariespp 19-68
Chapter 3 – Background-Induced Iteration Strategiespp 69-100
Chapter 4 – More Mice and Iteration Treespp 101-202
Chapter 5 – Some Properties of Induced Strategiespp 203-220
Chapter 6 – Normalizing Stacks of Iteration Treespp 221-290
Chapter 7 – Strategies That Condense and Normalize Wellpp 291-340
Chapter 8 – Comparing Iteration Strategiespp 341-386
Chapter 9 – Fine Structure for the Least Branch Hierarchypp 387-440
Chapter 10 – Phalanx Iteration Into a Constructionpp 441-500
Chapter 11 – Hod in the Derived Model of a Hod Mousepp 501-526
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