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Transactions of the American Mathematical Society

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The number of certain integral polynomials and nonrecursive sets of integers, Part 2


Author: Harvey M. Friedman
Journal: Trans. Amer. Math. Soc. 357 (2005), 1013-1023
MSC (2000): Primary 03D20, 03D80; Secondary 11U05
DOI: https://doi.org/10.1090/S0002-9947-04-03632-3
Published electronically: October 5, 2004
MathSciNet review: 2110430
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Abstract | References | Similar Articles | Additional Information

Abstract: We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, from recursion theory, and from the negative solution to Hilbert's 10th Problem.


References [Enhancements On Off] (What's this?)

  • 1. Piergiorgio Odifreddi, Classical recursion theory, Studies in Logic and the Foundations of Mathematics, vol. 125, North-Holland Publishing Co., Amsterdam, 1989. The theory of functions and sets of natural numbers; With a foreword by G. E. Sacks. MR 982269
  • 2. Handbook of mathematical logic, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Edited by Jon Barwise; With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra; Studies in Logic and the Foundations of Mathematics, Vol. 90. MR 0457132
  • 3. T. Erdélyi, H. Friedman, The number of certain integral polynomials and nonrecursive sets of integers, Part 1, this issue.
  • 4. Hilary Putnam, An unsolvable problem in number theory, J. Symbolic Logic 25 (1960), 220–232. MR 0158825, https://doi.org/10.2307/2964679

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Additional Information

Harvey M. Friedman
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: friedman@math.ohio-state.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03632-3
Received by editor(s): July 15, 2003
Published electronically: October 5, 2004
Article copyright: © Copyright 2004 American Mathematical Society