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A strongly minimal expansion of (ω, s)

Published online by Cambridge University Press:  12 March 2014

David Marker
David Marker*
Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60680
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Extract

We will show that there is a nontrivial strongly minimal expansion of (ω, s), the natural numbers with successor. Pillay and Steinhorn [1] proved that there is no -minimal expansion of (ω, ≤). This result provides an interesting contrast.

The strongly minimal expansion of (ω, s) is very easy to describe. Consider the order-two permutation of ω, π recursively defined by

Let T be Th(ω, s, π, 0).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 1 , March 1987 , pp. 205 - 207
Copyright
Copyright © Association for Symbolic Logic 1987

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References

REFERENCE

[1] Pillay, A. and Steinhorn, C., Discrete o-minimal structures, preprint.Google Scholar