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Definability with a predicate for a semi-linear set

Published online by Cambridge University Press:  12 March 2014

Michael Benedikt  and
H. Jerome Keisler
Michael Benedikt
Affiliation:
Bell Laboratories, 2701 Lucent Lane, Lisle, IL 60532, USA, E-mail: benedikt@research.bell-labs.com
H. Jerome Keisler
Affiliation:
University of Wisconsin-Madison, Department of Mathematics Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388, USA, E-mail: keisler@math.wisc.edu, URL: http://www.math.wisc.edu/~keisler
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Abstract

We settle a number of questions concerning definability in first order logic with an extra predicate symbol ranging over semi-linear sets. We give new results both on the positive and negative side: we show that in first-order logic one cannot query a semi-linear set as to whether or not it contains a line, or whether or not it contains the line segment between two given points. However, we show that some of these queries become definable if one makes small restrictions on the semi-linear sets considered.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 1 , March 2003 , pp. 319 - 351
Copyright
Copyright © Association for Symbolic Logic 2003

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References

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