## Reverse Mathematics 2001

Stephen G. Simpson , editor

Year: 2005

ISBN: 1-56881-264-7

416 pages. Paperback.

Year: 2005

ISBN:1-56881-263-9

416 pages. Hardcover.

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.

### 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 - António 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