Book contents
- Frontmatter
- Preface
- Contents
- Possible m-diagrams ofmodels of arithmetic
- Weak theories of nonstandard arithmetic and analysis
- Notions of compactness in weak subsystems of second order arithmetic
- Proof-theoretic strength of the stable marriage theorem and other problems
- Free sets and reversemathematics
- Interpreting arithmetic in the r.e. degrees under Σ4-induction
- Reverse mathematics, Archimedean classes, and Hahn's Theorem
- The Baire category theoremover a feasible base theory
- Basic applications of weak König's lemma in feasible analysis
- Maximal nonfinitely generated subalgebras
- Metamathematics of comparability
- A note on compactness of countable sets
- A survey of the reversemathematics of ordinal arithmetic
- Reversemathematics and ordinal suprema
- Did Cantor need set theory?
- Models of arithmetic: quantifiers and complexity
- Higher order reversemathematics
- Arithmetic saturation
- WQO and BQO theory in subsystems of second order arithmetic
- Reverse mathematics and graph coloring: eliminating diagonalization
- Undecidable theories and reversemathematics
- Π01 sets and models of WKL0
- Manipulating the reals in RCA0
- Reverse mathematics and weak systems of 0-1 strings for feasible analysis
- References
Reversemathematics and ordinal suprema
Published online by Cambridge University Press: 31 March 2017
Edited by
Book contents
- Frontmatter
- Preface
- Contents
- Possible m-diagrams ofmodels of arithmetic
- Weak theories of nonstandard arithmetic and analysis
- Notions of compactness in weak subsystems of second order arithmetic
- Proof-theoretic strength of the stable marriage theorem and other problems
- Free sets and reversemathematics
- Interpreting arithmetic in the r.e. degrees under Σ4-induction
- Reverse mathematics, Archimedean classes, and Hahn's Theorem
- The Baire category theoremover a feasible base theory
- Basic applications of weak König's lemma in feasible analysis
- Maximal nonfinitely generated subalgebras
- Metamathematics of comparability
- A note on compactness of countable sets
- A survey of the reversemathematics of ordinal arithmetic
- Reversemathematics and ordinal suprema
- Did Cantor need set theory?
- Models of arithmetic: quantifiers and complexity
- Higher order reversemathematics
- Arithmetic saturation
- WQO and BQO theory in subsystems of second order arithmetic
- Reverse mathematics and graph coloring: eliminating diagonalization
- Undecidable theories and reversemathematics
- Π01 sets and models of WKL0
- Manipulating the reals in RCA0
- Reverse mathematics and weak systems of 0-1 strings for feasible analysis
- References
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- Reverse Mathematics 2001 , pp. 235 - 243Publisher: Cambridge University PressPrint publication year: 2005
References
[1] , Beiträge zur Begründung der transfinitenMengenlehre, Mathematische Annalen., vol. 49 (1897), pp. 207–246, English translation by published as Contributions to the founding of the theory of transfinite numbers, Dover, New York, 1955.
[2] , Systems of second order arithmetic with restricted induction, I, II (abstracts), The Journal of Symbolic Logic, vol. 41 (1976), pp. 557–559.
[3] and , Weak comparability of well orderings and reverse mathematics,Annals of Pure and Applied Logic, vol. 47 (1990), pp. 11–29.
[4] , Reverse mathematics and ordinal exponentiation,Annals of Pure and Applied Logic, vol. 66 (1994), pp. 1–18.
[5] , Ordinal inequalities, transfinite induction, and reverse mathematics,The Journal of Symbolic Logic, vol. 64 (1999), pp. 769–774.
[6] , A survey of the reverse mathematics of ordinal arithmetic,Reverse mathematics 2001 (, editor), Lecture Notes in Logic, vol. 22, , 2005, this volume, pp. 222–234.Google Scholar
[7] , , and , On series of ordinals and combinatorics,Mathematical Logic Quarterly, vol. 43 (1997), pp. 121–133.
[8] , Cardinal and ordinal numbers, Polska Akademia Nauk, Monografie Matematyczne. Tom 34, Państwowe Wydawnictwo Naukowe, Warsaw, 1958.
[9] , Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin/Heidelberg, 1999.
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