The Core Model

A. Dodd

doi:10.1017/CBO9780511600586

The Core Model

The core model, K, is a generalization of Gödel's constructible universe of set theory; K is used to produce 'fine structural' results of a less restrictive kind. This book aims to introduce the core model to those with a basic knowledge of axiomatic set theory. The covering lemma for K is the main technical result but other applications are also considered. The author gives a full exposition of general fine structure and of iterated ultrapowers and concludes the work with a short section on the difficulties encountered in constructing more general core models using 'extenders'.

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The Core Model

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

PRELIMINARIES
pp ix-xiii

INTRODUCTION
pp xiv-xxxviii

I - FINE STRUCTURE
pp 1-1

1 - A weak set theory
pp 2-9

2 - Relative constructibility
pp 10-21

3 - Acceptability and the projectum
pp 22-30

4 - Models of R
pp 31-39

II - NORMAL MEASURES
pp 40-40

5 - Normal measures and ultrapowers
pp 41-48

6 - Iterated ultrapowers
pp 49-53

7 - Indiscernibles
pp 54-59

8 - Iterability
pp 60-68

III - MICE
pp 69-69

9 - Mice
pp 70-75

10 - Properties of mice
pp 76-85

11 - Acceptability revisited
pp 86-94

12 - O#
pp 95-103

13 - The model L[U]
pp 104-113

IV - THE CORE MODEL
pp 114-114

14 - The core model
pp 115-119

15 - Examples of K
pp 120-127

16 - Embeddings of K
pp 128-136

17 - Applications of K
pp 137-143

V - THE COVERING LEMMA
pp 144-144

18 - The upward mapping theorem
pp 145-159

19 - The covering lemma
pp 160-168

20 - L[U] and L[U,C]
pp 169-176

21 - Applications of the covering lemma
pp 177-185

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The Core Model

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