Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 68, Issue 1 (2003), 319-351.
Definability with a predicate for a semi-linear set
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.
J. Symbolic Logic, Volume 68, Issue 1 (2003), 319-351.
First available in Project Euclid: 21 February 2003
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Benedikt, Michael; Keisler, H. Jerome. Definability with a predicate for a semi-linear set. J. Symbolic Logic 68 (2003), no. 1, 319--351. doi:10.2178/jsl/1045861516. https://projecteuclid.org/euclid.jsl/1045861516