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Perspectives in Logic

Admissible Sets and Structures: An Approach to Definability Theory

Jon Barwise

Perspectives in Mathematical Logic, Volume 7
Berlin: Springer-Verlag, 1975.
394 pp.

Subjects:

02F27 (primary)
02B25 (primary)
O2H10 (primary)
O2K35 (primary)
Permanent link to this monograph: http://projecteuclid.org/euclid.pl/1235418470
Mathmatical Reviews number (MathSciNet): MR0424560
ISBN:3-540-07451-1
ISBN:0-387-07451-1

Copyright © 1975, Association for Symbolic Logic.

Miscellaneous Frontmatter

Introduction

1-4

Part A: The Basic Theory

Chapter I: Admissible Set Theory

7-41

Chapter II: Some Admissible Sets

42-77

Chapter III: Countable Fragments of $\mathsf{L}_{\infty\omega}$

78-112

Chapter IV: Elementary Results on $\mathbb{H}YP_{\mathfrak{M}}$

113-149

Part B: The Absolute Theory

Chapter V: The Recursion Theory of $\Sigma_1$ Predicates on Admissible Sets

153-196

Chapter VI: Inductive Definitions

197-254

Part C: Towards a General Theory

Chapter VII: More about $\mathsf{L}_{\infty\omega}$

257-310

Chapter VIII: Strict $\Pi^{1}-{1}$ Predicates and Konig Principles

311-364

Appendix: Nonstandard Compactness Arguments and the Admissible Cover

365-379

References

380-385

Index of Notation

386-387

Subject Index

388-394

Miscellaneous Backmatter