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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $\Pi _{3}$-theory of the computably enumerable
Turing degrees is undecidable


Authors: Steffen Lempp, André Nies and Theodore A. Slaman
Journal: Trans. Amer. Math. Soc. 350 (1998), 2719-2736
MSC (1991): Primary 03D25, 03D35
MathSciNet review: 1389784
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Abstract: We show the undecidability of the $\Pi _{3}$-theory of the partial order of computably enumerable Turing degrees.


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Additional Information

Steffen Lempp
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706–1388
Email: lempp@math.wisc.edu

André Nies
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1514
Email: nies@math.uchicago.edu

Theodore A. Slaman
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-0001
Email: slaman@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01800-5
PII: S 0002-9947(98)01800-5
Keywords: (Computably, recursively) enumerable degrees, $\Pi _{3}$-theory, fragment of first-order theory, undecidability
Received by editor(s): December 20, 1995
Additional Notes: The first author’s research was partially supported by NSF Grants DMS-9100114 and DMS-9504474. The second author’s research was partially supported by NSF Grant DMS-9500983. The third author’s research was partially supported by NSF Grant DMS-9500878.
Article copyright: © Copyright 1998 American Mathematical Society