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

DOI:
https://doi.org/10.1090/S0002-9939-99-04920-5

Published electronically:
May 6, 1999

MathSciNet review:
1610909

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-99-04920-5

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