Reverse Mathematics 2001
Published on 9. April 2020
978-1-108-63722-0 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 7 Line drawings, black and white
File size
0,00 MB
ISBN-13
978-1-108-63722-0 (9781108637220)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
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).
Content
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 ?4-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 Antonio M. Fernandes; 9. Basic applications of weak Koenig's lemma in feasible analysis Antonio 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. ?01 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.
