On the computability-theoretic complexity of trivial, strongly minimal models
Authors:
Bakhadyr M. Khoussainov, Michael C. Laskowski, Steffen Lempp and Reed Solomon
Journal:
Proc. Amer. Math. Soc. 135 (2007), 3711-3721
MSC (2000):
Primary 03C57; Secondary 03D45
DOI:
https://doi.org/10.1090/S0002-9939-07-08865-X
Published electronically:
June 21, 2007
MathSciNet review:
2336588
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Abstract | References | Similar Articles | Additional Information
Abstract: We show the existence of a trivial, strongly minimal (and thus uncountably categorical) theory for which the prime model is computable and each of the other countable models computes . This result shows that the result of Goncharov/Harizanov/Laskowski/Lempp/McCoy (2003) is best possible for trivial strongly minimal theories in terms of computable model theory. We conclude with some remarks about axiomatizability.
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Additional Information
Bakhadyr M. Khoussainov
Affiliation:
Department of Computer Science, University of Auckland, Auckland, New Zealand
Email:
bmk@cs.auckland.ac.nz
Michael C. Laskowski
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email:
mcl@math.umd.edu
Steffen Lempp
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
lempp@math.wisc.edu
Reed Solomon
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email:
solomon@math.uconn.edu
DOI:
https://doi.org/10.1090/S0002-9939-07-08865-X
Keywords:
Computable model,
uncountably categorical,
strongly minimal,
trivial geometry,
axiomatizability
Received by editor(s):
December 14, 2005
Received by editor(s) in revised form:
January 19, 2006, and August 4, 2006
Published electronically:
June 21, 2007
Additional Notes:
The first author’s research was partially supported by The Marsden Fund of New Zealand.
The second author’s research was partially supported by NSF grant DMS-0300080.
The third author’s research was partially supported by NSF grant DMS-0140120.
The fourth author’s research was partially supported by NSF grant DMS-0400754.
Communicated by:
Julia Knight
Article copyright:
© Copyright 2007
American Mathematical Society