Time and Place: Th 11:00AM - 1:00PM, 736 Evans
Course Control Number: 54824
Reading List: [pdf]
| [1] | C. Dimitracopoulos and J. Paris. The pigeonhole principle and fragments of arithmetic. Z. Math. Logik Grundlag. Math., 32(1):73–80, 1986. [Publisher's site] |
| [2] | J. Paris, A. Wilkie, and A. Woods. Provability of the Pigeonhole Principle and the Existence of Infinitely Many Primes. The Journal of Symbolic Logic, 53(4):1235–1244, 1988. [Publisher's site] |
| [3] | J. Paris and A. Wilkie. Counting problems in bounded arithmetic. In Methods in mathematical logic (Caracas, 1983), volume 1130 of Lecture Notes in Math., pages 317–340. Springer, Berlin, 1985. [Publisher's site] |
| [4] | J. Paris and A. Wilkie. Counting Δ0 sets. Fund. Math., 127(1):67–76, 1987. [Publisher's site] |
| [5] | J. Paris and L. Harrington. A mathematical incompleteness in Peano arithmetic. In J. Barwise, editor, Handbook of Mathematical Logic, pages 1133–1142. North-Holland, Amsterdam, 1977. |
| [6] | Peter A. Cholak, Carl G. Jockusch, and Theodore A. Slaman. On the strength of Ramsey's theorem for pairs. J. Symbolic Logic, 66(1):1–55, 2001. [Preprint version] |
| [7] | Timothy J. Carlson and Stephen G. Simpson. A dual form of Ramsey's theorem. Adv. in Math., 53(3):265–290, 1984. [Publisher's site] |
| [8] | Stephen G. Simpson. Recursion theoretic aspects of the dual Ramsey theorem. In Recursion theory week (Oberwolfach, 1984), volume 1141 of Lecture Notes in Math., pages 357–371. Springer, Berlin, 1985. [Publisher's site] |
| [9] | Joseph S. Miller and Reed Solomon. Effectiveness for infinite variable words and the dual Ramsey theorem. Arch. Math. Logic, 43(4):543–555, 2004. [Preprint Version] |
| [10] | Timothy J. Carlson. Some unifying principles in Ramsey theory. Discrete Math., 68(2-3):117–169, 1988. [Publisher's site] |
| [11] | Stephen G. Simpson. Nonprovability of certain combinatorial properties of finite trees. In Harvey Friedman's research on the foundations of mathematics, volume 117 of Stud. Logic Found. Math., pages 87–117. North-Holland, Amsterdam, 1985. |
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