Coding the Universe

A. Beller; R. Jensen; P. Welch

doi:10.1017/CBO9780511629198

Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another model L[a] with the same properties. L[a] is Gödels universe of 'constructible' sets L, together with a set of integers a which code all the cardinality and cofinality structure of M. Some applications are also considered. Graduate students and research workers in set theory and logic will be especially interested by this account.

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Coding the Universe

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

0 - An introduction
pp 1-6

1 - The building blocks
pp 7-25

2 - The conditions
pp 26-72

3 - Distributivity
pp 73-120

4 - The dénouement
pp 121-154

5 - Applications
pp 155-194

6 - The fine-structural lemmas
pp 195-244

7 - The Cohen-generic sets
pp 245-255

8 - How to get rid of “⌉0#”
pp 256-307

9 - Some further applications
pp 308-327

Appendix
pp 328-346

Bibliography
pp 347-348

Notational index
pp 349-351

Index
pp 352-353

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Coding the Universe

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