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Reverse Mathematics 2001

Reverse Mathematics 2001

$105.00 ( ) USD

Part of Lecture Notes in Logic

Andrew Arana, Jeremy Avigad, Douglas K. Brown, Douglas Cenzer, Jeffrey B. Remmel, Peter A. Cholak, Mariagnese Giusto, Jeffry L. Hirst, Carl G. Jockusch, Jr, C. T. Chong, Richard A. Shore, Yue Yang, Rodney G. Downey, Reed Solomon, António M. Fernandes, Fernando Ferreira, Harvey M. Friedman, A. James Humphreys, Julia F. Knight, Ulrich Kohlenbach, Roman Kossak, Alberto Marcone, James H. Schmerl, Stephan G. Simpson, Kazuyuki Tanaka, Takeshi Yamazaki
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  • Publication planned for: April 2020
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108637220

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About the Authors
  • 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.

    • Contains twenty-four original research papers by leading experts
    • Serves as a sequel and update of the author's Subsystems of Second Order Arithmetic (2nd edition, Cambridge, 2009)
    • Suitable for graduate students and researchers in mathematical logic
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    Product details

    • Publication planned for: April 2020
    • format: Adobe eBook Reader
    • isbn: 9781108637220
    • contains: 7 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    1. Possible m-diagrams of models of arithmetic Andrew Arana
    2. Weak theories of nonstandard arithmetic and analysis Jeremy Avigad
    3. Notions of compactness in weak subsystems of second order arithmetic Douglas K. Brown
    4. Proof theoretic strength of the stable marriage theorem and other problems Douglas Cenzer and Jeffrey B. Remmel
    5. Free sets and reverse mathematics Peter A. Cholak, Mariagnese Giusto, Jeffry L. Hirst and Carl G. Jockusch, Jr
    6. Interpreting arithmetic in the r.e. degrees under Σ4-induction C. T. Chong, Richard A. Shore and Yue Yang
    7. Reverse mathematics, Archimedean classes, and Hahn's theorem Rodney G. Downey and Reed Solomon
    8. The Baire category theorem over a feasible base theory António M. Fernandes
    9. Basic applications of weak König's lemma in feasible analysis António M. Fernandes and Fernando Ferreira
    10. Maximal nonfinitely generated subalgebras Harvey M. Friedman
    11. Metamathematics of comparability Harvey M. Friedman
    12. A note on compactness of countable sets Jeffry L. Hirst
    13. A survey of the reverse mathematics of ordinal arithmetic Jeffry L. Hirst
    14. Reverse mathematics and ordinal suprema Jeffry L. Hirst
    15. Did Cantor need set theory? A. James Humphreys
    16. Models of arithmetic: quantifiers and complexity Julia F. Knight
    17. Higher order reverse mathematics Ulrich Kohlenbach
    18. Arithmetic saturation Roman Kossak
    19. WQO and BQO theory in subsystems of second order arithmetic Alberto Marcone
    20. Reverse mathematics and graph coloring: eliminating diagonalization James H. Schmerl
    21. Undecidable theories and reverse mathematics James H. Schmerl
    22. Π01 and models of WKL0 Stephan G. Simpson
    23. Manipulating the reals in RCA0 Kazuyuki Tanaka and Takeshi Yamazaki
    24. Reverse mathematics and weak systems of 0-1 strings for feasible analysis Takeshi Yamazaki.

  • Editor

    Stephen G. Simpson, Pennsylvania State University
    Stephen G. Simpson is a Professor in the Mathematics Department at Pennsylvania State University. He specializes in mathematical logic and foundations of mathematics, and he has authored or edited a number of books, including Subsystems of Second Order Arithmetic (Cambridge, 2010) and Logic and Combinatorics (1987).

    Contributors

    Andrew Arana, Jeremy Avigad, Douglas K. Brown, Douglas Cenzer, Jeffrey B. Remmel, Peter A. Cholak, Mariagnese Giusto, Jeffry L. Hirst, Carl G. Jockusch, Jr, C. T. Chong, Richard A. Shore, Yue Yang, Rodney G. Downey, Reed Solomon, António M. Fernandes, Fernando Ferreira, Harvey M. Friedman, A. James Humphreys, Julia F. Knight, Ulrich Kohlenbach, Roman Kossak, Alberto Marcone, James H. Schmerl, Stephan G. Simpson, Kazuyuki Tanaka, Takeshi Yamazaki

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