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Lecture Notes in Logic, 21
Reverse Mathematics 2001

 

Stephen G. Simpson , editor

 

Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting recent developments in reverse mathematics and subsystems of second order arithmetic.

Year: 2005
Price:$40.00
ISBN: 1-56881-264-7
416 pages. Paperback.
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Year: 2005
Price:$70.00 ISBN:1-56881-263-9
416 pages. Hardcover.

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Table of Contents

Preface

Andrew Arana
Possible m-diagrams of models of arithmetic

Jeremy Avigad
Weak theories of nonstandard arithmetic and analysis

Douglas K. Brown
Notions of compactness in weak subsystems of secord order arithmetic

Douglas Cenzer and Jeffrey B. Remmel
Proof-theoretic strength of the stable marriage theorem and other problems

Peter A. Cholak, Mariagnese Giusto, Jeffry L. Hirst, and Carl G. Jockusch, Jr.
Free sets and reverse mathematics

C.T. Chong, Richard A. Shore, and Yue Yang
Interepreting arithmetic in the r.e. degrees under $\Signma_4$-induction

Rodney G. Downey and Reed Solomon
Reverse mathematics, Archimedean classes, and Hahn's Theorem

Antó
nio M. Fernandes
The Baire category theorem over a feasible base theory

Harvy M. Friedman
Maximal nonfinitely generated subalgebras

Harvey M. Friedman
Metamathematics of comparability

Jeffry L. Hirst
A note on compactness of countable sets

Jeffry L. Hirst
A survey of the reverse mathematics of ordinal arithmetic

Jeffry L. Hirst
Reverse mathematics and ordinal suprema

A. James Humphreys
Did Cantor need set theory?

Julia F. Knight
Models of arithmetic: quantifiers and complexity

Ulrich Kohlenbach
Higher order reverse mathematics

Roman Kossak
Arithmetic saturation

Alberto Marcone
WQO and BQO theory in subsystems of second order arithmetic

James H. Schmerl
Reverse mathematics and graph coloring:eliminating diagonalization

James H. Schmerl
Undecidable theories and reverse mathematics

Stephen G. Simpson
$\Pi^0_1$ sets and models of $WKL_0$

Kazuyuki Tanaka and Takeshi Yamazaki
Manipulating the reals in $RCA_0$

Takeshi Yamazaki
Reverse mathematics and wek systems of 0-1 strings for feasible analysis



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