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Constructive models of uncountably categorical theories
Author(s):
Bernhard
Herwig;
Steffen
Lempp;
Martin
Ziegler
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3711-3719.
MSC (1991):
Primary 03C57, 03D45
Posted:
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.
References:
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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:
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
Posted:
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.
Copyright of article:
Copyright
1999,
American Mathematical Society
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