Reverse Mathematics 2001

doi:10.1017/9781316755846

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Reverse mathematics is a program of research in the foundations of mathematics, motivated by two foundational questions: 'what are appropriate axioms for mathematics?' and 'what are the logical strengths of particular axioms and particular theorems?' This volume, the twenty-first publication in the Lecture Notes in Logic series, contains twenty-four original research papers from respected authors that present exciting new developments in reverse mathematics and subsystems of second order arithmetic since 1998.

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Contents

Frontmatter
pp i-iv
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Preface
pp v-viii
- By Stephen G. Simpson, Pennsylvania State University
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Contents
pp ix-x
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Possible m-diagrams ofmodels of arithmetic
pp 1-18
- By Andrew Arana
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Weak theories of nonstandard arithmetic and analysis
pp 19-46
- By Jeremy Avigad
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Notions of compactness in weak subsystems of second order arithmetic
pp 47-66
- By Douglas K. Brown
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Proof-theoretic strength of the stable marriage theorem and other problems
pp 67-103
- By Douglas Cenzer, Jeffrey B. Remmel
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Free sets and reversemathematics
pp 104-119
- By Peter A. Cholak, Mariagnese Giusto, Jeffry L. Hirst, Carl G. Jockusch
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Interpreting arithmetic in the r.e. degrees under Σ4-induction
pp 120-146
- By C. T. Chong, Richard A. Shore, Yue Yang
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Reverse mathematics, Archimedean classes, and Hahn's Theorem
pp 147-163
- By Rodney G. Downey, Reed Solomon
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The Baire category theoremover a feasible base theory
pp 164-174
- By António M. Fernandes
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Basic applications of weak König's lemma in feasible analysis
pp 175-188
- By António M. Fernandes, Fernando Ferreira
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Maximal nonfinitely generated subalgebras
pp 189-200
- By Harvey M. Friedman
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Metamathematics of comparability
pp 201-218
- By Harvey M. Friedman
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A note on compactness of countable sets
pp 219-221
- By Jeffry L. Hirst
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A survey of the reversemathematics of ordinal arithmetic
pp 222-234
- By Jeffry L. Hirst
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Reversemathematics and ordinal suprema
pp 235-243
- By Jeffry L. Hirst
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Did Cantor need set theory?
pp 244-270
- By A. James Humphreys
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Models of arithmetic: quantifiers and complexity
pp 271-280
- By Julia F. Knight
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Higher order reversemathematics
pp 281-295
- By Ulrich Kohlenbach
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Arithmetic saturation
pp 296-302
- By Roman Kossak
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WQO and BQO theory in subsystems of second order arithmetic
pp 303-330
- By Alberto Marcone
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Reverse mathematics and graph coloring: eliminating diagonalization
pp 331-348
- By James H. Schmerl
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Undecidable theories and reversemathematics
pp 349-351
- By James H. Schmerl
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Π01 sets and models of WKL0
pp 352-378
- By Stephen G. Simpson
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Manipulating the reals in RCA0
pp 379-393
- By Kazuyuki Tanaka, Takeshi Yamazaki
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Reverse mathematics and weak systems of 0-1 strings for feasible analysis
pp 394-401
- By Takeshi Yamazaki
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Reverse Mathematics 2001

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Contents

Frontmatter
pp i-iv

Preface
pp v-viii

Contents
pp ix-x

Possible m-diagrams ofmodels of arithmetic
pp 1-18

Weak theories of nonstandard arithmetic and analysis
pp 19-46

Notions of compactness in weak subsystems of second order arithmetic
pp 47-66

Proof-theoretic strength of the stable marriage theorem and other problems
pp 67-103

Free sets and reversemathematics
pp 104-119

Interpreting arithmetic in the r.e. degrees under Σ4-induction
pp 120-146

Reverse mathematics, Archimedean classes, and Hahn's Theorem
pp 147-163

The Baire category theoremover a feasible base theory
pp 164-174

Basic applications of weak König's lemma in feasible analysis
pp 175-188

Maximal nonfinitely generated subalgebras
pp 189-200

Metamathematics of comparability
pp 201-218

A note on compactness of countable sets
pp 219-221

A survey of the reversemathematics of ordinal arithmetic
pp 222-234

Reversemathematics and ordinal suprema
pp 235-243

Did Cantor need set theory?
pp 244-270

Models of arithmetic: quantifiers and complexity
pp 271-280

Higher order reversemathematics
pp 281-295

Arithmetic saturation
pp 296-302

WQO and BQO theory in subsystems of second order arithmetic
pp 303-330

Reverse mathematics and graph coloring: eliminating diagonalization
pp 331-348

Undecidable theories and reversemathematics
pp 349-351

Π01 sets and models of WKL0
pp 352-378

Manipulating the reals in RCA0
pp 379-393

Reverse mathematics and weak systems of 0-1 strings for feasible analysis
pp 394-401

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