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

 

Constructive models
of uncountably categorical theories


Authors: Bernhard Herwig, Steffen Lempp and Martin Ziegler
Journal: Proc. Amer. Math. Soc. 127 (1999), 3711-3719
MSC (1991): Primary 03C57, 03D45
Published electronically: May 6, 1999
MathSciNet review: 1610909
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Abstract: We construct a strongly minimal (and thus uncountably categorical) but not totally categorical theory in a finite language of binary predicates whose only constructive (or recursive) model is the prime model.


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Additional Information

Bernhard Herwig
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, England
Address at time of publication: Institut für Mathematische Logik, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
Email: herwig@amsta.leeds.ac.uk, herwig@ruf.uni-freiburg.de

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

Martin Ziegler
Affiliation: Institut für Mathematische Logik, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
Email: ziegler@uni-freiburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04920-5
PII: S 0002-9939(99)04920-5
Keywords: Constructive/recursive/computable model, uncountably categorical first-order theory, strongly minimal set, unsolvable word problem, Cayley graph
Received by editor(s): October 20, 1997
Received by editor(s) in revised form: February 20, 1998
Published electronically: May 6, 1999
Additional Notes: The first author was supported by a grant of the British Engineering and Physical Sciences Research Council (Research Grant no. GR/K60503)
The second author’s research was partially supported by NSF grant DMS-9504474 and a grant of the British Engineering and Physical Sciences Research Council (Research Grant no. GR/K60497).
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 1999 American Mathematical Society