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.

**1.**P. Odifreddi, Classical Recursion Theory, Studies in Logic and the Foundations of Mathematics, volume 125, North-Holland, 1989. MR**90d:03072****2.**M. Davis, Unsolvable problems, in Jon Barwise, editor, Handbook of Mathematical Logic, volume 90 of Studies in Logic and the Foundations of Mathematics, Chapter C.2, pages 567-594, North Holland, 1977. MR**56:15351****3.**T. Erdélyi, H. Friedman, The number of certain integral polynomials and nonrecursive sets of integers, Part 1, this issue.**4.**H. Putnam, An unsolvable problem in number theory, Journal of Symbolic Logic, Vol. 25, No. 3, Sept. 1960, 220-232. MR**28:2048**

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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