￼￼￼￼￼Foreword

Contributors

PART A: MODEL THEORY

Guide to Part A

A.l. An introduction to first-order logic, Jon Barwise

A.2. Fundamentals of model theory, H. Jerome Keisler

A.3. Ultraproducts for algebraists, Paul C. Eklof

A.4. Model completeness, Angus Macintyre

A.5. Homogenous sets, Michael Morley

A.6. Infinitesimal analysis of curves and surfaces, K. D. Stroyan

A.7. Admissible sets and infinitary logic, M. Makkai

A.8. Doctrinesincategoricallogic,A.Kock andG.E.Reyes

PART B: SET THEORY

Guide to Part B

B.1. Axioms of set theory, J.R.Shoenfield

B.2. About the axiom of choice, ThomasJ. Jech

B.3. Combinatorics, Kenneth Kunen

B.4. Forcing,JohnP.Burgess

B.5. Constructibility, Keith J. Deulin

B.6. Martin’s Axiom, Mary Ellen Rudin

B.7. Consistency results in topology, I. Juhasrz

PART C: RECURSION THEORY

Guide to Part C

C.l. Elements of recursion theory, Herbert B. Enderton

C.2. Unsolvable problems. Martin Davis

C.3. Decidable theories. Michael O. Rabin

C.4. Degrees of unsolvability: a survey of results. Stephen G. Simpson

C.5. a-recursion theory. Richard A. Shore

C.6. Recursion in higher types. Alexander Kechris and Yiannis N. Moschovakis

C.7. An introduction to inductive definitions, Peter Aczel

C.8. Descriptive set theory: Projective sets, Donald A. Martin

PART D: PROOF THEORY AND CONSTRUCTIVE MATHEMATICS

Guide to Part D

D.l. The incompleteness theorems. C. Smorynski

D.2. Proof theory: Some applications of cut-elimination, Helmut Schwichtenberg

D.3. Herbrand’s Theorem and Gentzen’s notion of a direct proof, Richard Statman

D.4. Theories of finite type related to mathematical practice, Solomon Feferman

D.5. Aspects of constructive mathematics. A. S. Troelstra

D.6. The logic of topoi, Michael P. Fourman

D.7. The type free lambda calculus, Henk Barendregt

D.8. A mathematical incompleteness in Peano Arithmetic, Jeff Paris and Leo Harrington

Author Index

Subject Index

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