Lecture Notes in Logic, 21

Reverse Mathematics 2001

Stephen G. Simpson , editor

Year: 2005
ISBN: 1-56881-264-7
416 pages. Paperback.

Year: 2005
416 pages. Hardcover.

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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