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
Proof-theoretic strength of the stable marriage theorem and other problems
Published online by Cambridge University Press: 31 March 2017
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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. 67 - 103Publisher: Cambridge University PressPrint publication year: 2005
References
[1] , , and , On the strength of König's duality theorem for infinite bipartite graphs,Journal of Combinatorial Theory. Series B, vol. 54 (1992), no. 2, pp. 257–290.
[2] and , Reverse mathematics of some topics from algorithmic graph theory,Fundamenta Mathematicae, vol. 157 (1998), no. 1, pp. 1–13.
[3] , A decomposition theorem for partially ordered sets,Annals ofMathematics. Second Series, vol. 51 (1950), pp. 161–166.
[4] and , Partially ordered sets,American Journal ofMathematics, vol. 63 (1941), pp. 600–610.
[5] and , College admissions and the stability of marriage,American Mathematical Monthly, vol. 69 (1962), pp. 9–15.
[6] and , Reverse mathematics and recursive graph theory,MLQ. Mathematical Logic Quarterly, vol. 44 (1998), no. 4, pp. 465–473.
[7] , Combinatorics in subsystems of second order arithmetic, Ph.D. thesis, Pennsylvania State University, 1987.
[8] , Marriage theorems and reverse mathematics,Logic and computation (Pittsburgh, PA, 1987), Contemp. Math., vol. 106, Amer. Math. Soc., Providence, RI, 1990, pp. 181–196.
[9] , Reverse mathematics and rank functions for directed graphs,Archive for Mathematical Logic, vol. 39 (2000), no. 8, pp. 569–579.
[10] , Reverse mathematics and rank functions for directed graphs,Archive for Mathematical Logic, vol. 39 (2000), no. 8, pp. 569–579.
[11] , Recursive and on-line graph coloring,Handbook of recursive mathematics, vol. 2(, , , and , editors), Stud. Logic Found. Math., vol. 139, North-Holland, Amsterdam, 1998, pp. 1233–1269.
[12] , An effective version of Dilworth's theorem,Transactions of the American Mathematical Society, vol. 268 (1981), no. 1, pp. 63–77.
[13] , , and , Jr., Recursive dimension for partially ordered sets,Order, vol. 1 (1984), no. 1, pp. 67–82.
[14] , Stable marriage and its relation to other combinatorial problems, CRM Proceedings & Lecture Notes, vol. 10, American Mathematical Society, Providence, RI, 1997.
[15] , Graph colorings and recursively bounded Π0/1 -classes,Annals of Pure and Applied Logic, vol. 32 (1986), no. 2, pp. 185–194.
[16] , On the strength of König's duality theorem for countable bipartite graphs,The Journal of Symbolic Logic, vol. 59 (1994), no. 1, pp. 113–123.
[17] , Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.
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