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ON THE STRENGTH OF TWO RECURRENCE THEOREMS

  • ADAM R. DAY (a1)
Abstract

This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes that one of these theorems, the existence of an almost periodic point, lies strictly between WKL and ACA (working over RCA0). This is the first example of a theorem with this property. It also shows the existence of an almost periodic point is conservative over RCA0 for ${\rm{\Pi }}_1^1$ -sentences.

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[1] Beiglböck, M. and Towsner, H., Transfinite approximation of Hindman’s theorem . Israel Journal of Mathematics, vol. 191 (2012), no. 1, pp. 4159.
[2] Blass, A. R., Hirst, J. L., and Simpson, S. G., Logical analysis of some theorems of combinatorics and topological dynamics. Logic and combinatorics (Arcata, Calif., 1985), Contemporary Mathematics, vol. 65, American Mathematical Society, Providence, RI, 1987, pp. 125–156.
[3] Friedman, H., Simpson, S. G., and Yu, X., Periodic points and subsystems of second-order arithmetic . Annals of Pure and Applied Logic, vol. 62 (1993), no. 1, pp. 5164. Logic Colloquium ’89 (Berlin).
[4] Montalbán, A., Open questions in reverse mathematics . Bulletin of Symbolic Logic, vol. 17 (2011), no. 3, pp. 431454.
[5] Simpson, S. G., Subsystems of Second Order Arithmetic. 2nd edition, Cambridge University Press, New York, 2009.
[6] Tao, T., Poincaré’s Legacies, Part I. American Mathematical Society, Providence, 2009.
[7] Towsner, H., A combinatorial proof of the dense Hindman’s theorem . Discrete Mathematics, vol. 311 (2011), no. 14, pp. 13801384.
[8] Towsner, H., Hindman’s theorem: an ultrafilter argument in second order arithmetic, this Journal, vol. 76 (2011), no. 1, pp. 353360.
[9] Towsner, H., A simple proof and some difficult examples for Hindman’s theorem . Notre Dame Journal of Formal Logic, vol. 53 (2012), no. 1, pp. 5365.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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