ABSTRACT

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.

chapter |18 pages

POSSIBLE m-DIAGRAMS OF MODELS OF ARITHMETIC

ByANDREW ARANA

chapter |37 pages

PROOF-THEORETIC STRENGTH OF THE STABLE MARRIAGE THEOREM AND OTHER PROBLEMS

ByDOUGLAS CENZER, JEFFREY B. REMMEL

chapter |16 pages

FREE SETS AND REVERSE MATHEMATICS

ByPETER A. CHOLAK, MARIAGNESE GIUSTO, JEFFRY L. HIRST, CARL G. JOCKUSCH

chapter |27 pages

INTERPRETING ARITHMETIC IN THE R.E. DEGREES UNDER Σ4-INDUCTION

ByC. T. CHONG, RICHARD A. SHORE, YUE YANG

chapter |17 pages

REVERSE MATHEMATICS, ARCHIMEDEAN CLASSES, AND HAHN'S THEOREM

ByRODNEY G. DOWNEY, REED SOLOMON

chapter |13 pages

THE BAIRE CATEGORY THEOREM OVER A FEASIBLE BASE THEORY

ByANTÓNIO M. FERNANDES

chapter |14 pages

BASIC APPLICATIONS OF WEAK KÖNIG'S LEMMA IN FEASIBLE ANALYSIS

ByANTONIO M. FERNANDES, FERNANDO FERREIRA

chapter |12 pages

MAXIMAL NONFINITELY GENERATED SUBALGEBRAS

ByHARVEY M. FRIEDMAN

chapter |18 pages

METAMATHEMATICS OF COMPARABILITY

ByHARVEY M. FRIEDMAN

chapter |3 pages

A NOTE ON COMPACTNESS OF COUNTABLE SETS

ByJEFFRY L. HIRST

chapter |9 pages

REVERSE MATHEMATICS AND ORDINAL SUPREMA

ByJEFFRY L. HIRST

chapter |27 pages

DID CANTOR NEED SET THEORY?

ByA. JAMES HUMPHREYS

chapter |11 pages

MODELS OF ARITHMETIC: QUANTIFIERS AND COMPLEXITY

ByJULIA F. KNIGHT

chapter |15 pages

HIGHER ORDER REVERSE MATHEMATICS

ByULRICH KOHLENBACH

chapter |7 pages

ARITHMETIC SATURATION

ByROMAN KOSSAK

chapter |3 pages

UNDECIDABLE THEORIES AND REVERSE MATHEMATICS

ByJAMES H. SCHMERL

chapter |27 pages

∏01 SETS AND MODELS OF WKL0

BySTEPHEN G. SIMPSON

chapter |15 pages

MANIPULATING THE REALS IN RCA0

ByKAZUYUKI TANAKA, TAKESHI YAMAZAKI