Journal of Symbolic Logic

Definability with a predicate for a semi-linear set

Michael Benedikt and H. Jerome Keisler

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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.

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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.

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