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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Prime models of theories of computable linear orderings


Author: Denis R. Hirschfeldt
Journal: Proc. Amer. Math. Soc. 129 (2001), 3079-3083
MSC (2000): Primary 03D45; Secondary 06A05, 03C57, 03C50, 03C65
Published electronically: February 22, 2001
MathSciNet review: 1840114
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Abstract:

We answer a long-standing question of Rosenstein by exhibiting a complete theory of linear orderings with both a computable model and a prime model, but no computable prime model. The proof uses the relativized version of the concept of limitwise monotonic function.


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Additional Information

Denis R. Hirschfeldt
Affiliation: School of Mathematical and Computing Sciences, Victoria University of Wellington, New Zealand
Address at time of publication: Department of Mathematics, The University of Chicago, Chicago, Illinois 60637-1538
Email: Denis.Hirschfeldt@mcs.vuw.ac.nz, drh@math.uchicago.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05923-8
PII: S 0002-9939(01)05923-8
Received by editor(s): December 29, 1999
Received by editor(s) in revised form: February 25, 2000
Published electronically: February 22, 2001
Additional Notes: The author’s research was supported by the Marsden Fund of New Zealand. The author thanks the anonymous referee for valuable historical comments.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2001 American Mathematical Society