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A new spectrum of recursive models using an amalgamation construction

Published online by Cambridge University Press:  12 March 2014

Uri Andrews
Uri Andrews*
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706-13886, USA, E-mail: andrews@math.wisc.edu
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Abstract

We employ an infinite-signature Hrushovski amalgamation construction to yield two results in Recursive Model Theory. The first result, that there exists a strongly minimal theory whose only recursively presentable models are the prime and saturated models, adds a new spectrum to the list of known possible spectra. The second result, that there exists a strongly minimal theory in a finite language whose only recursively presentable model is saturated, gives the second non-trivial example of a spectrum produced in a finite language.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 3 , September 2011 , pp. 883 - 896
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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