Journal of Symbolic Logic

Definability with a predicate for a semi-linear set

Michael Benedikt and H. Jerome Keisler

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 1 (2003), 319-351.

Dates
First available in Project Euclid: 21 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1045861516

Digital Object Identifier
doi:10.2178/jsl/1045861516

Mathematical Reviews number (MathSciNet)
MR1959322

Zentralblatt MATH identifier
1045.03032

Citation

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


Export citation

References

  • F. Afrati, T. Andronikos, and T. Kavalieros On the expressiveness of first-order constraint languages, Constraint databases and applications, ESPRIT CONTESSA workshop (G. M. Kuper and M. Wallace, editors), Lecture Notes in Computer Science, vol. 1034, Springer,1996, pp. 22--39.
  • F. Afrati, S. Cosmadakis, S. Grumbach, and G. Kuper Linear vs. polynomial constraints in database query languages, Proceedings of the second international workshop on principles and practice of constraint programming, Lecture Notes in Computer Science, vol. 874, Springer,1995, pp. 181--192.
  • M. Benedikt, G. Dong, L. Libkin, and L. Wong Relational expressive power of constraint query languages, Journal of the ACM, vol. 45 (1998), pp. 1--34.
  • M. Benedikt and H. J. Keisler Expressive power of unary counters, Structures in Logic and Computer Science (Mycielski, Rozenberg, and Salomaa, editors), Lecture Notes in Computer Science, vol. 1261, Springer,1997.
  • M. Benedikt and H. J. Keisler Definability over linear constraints, Computer science logic, CSL 2000 (P. Clote and H. Schwichtenberg, editors), Lecture Notes in Computer Science, vol. 1862, Springer,2000, pp. 217--231.
  • C.C. Chang and H.J. Keisler Model Theory, North Holland,1990.
  • O. Chapuis and P. Koiran Definability of geometric properties in algebraically closed fields, Mathematical Logic Quarterly, vol. 45 (1999), no. 4, pp. 533--550.
  • P. Kanellakis, G. Kuper, and P. Revesz Constraint query languages, Journal of Computer and System Sciences, vol. 51 (1995), pp. 26--52.
  • C. Karp Finite quantifier equivalence, The Theory of Models, North-Holland,1965, pp. 407--412.
  • B. Kuijpers, J. Paredaens, and J. Van den Bussche On topological elementary equivalence of spatial databases, Proceedings of the Sixth International Conference on Database Theory, Lecture Notes in Computer Science, vol. 1186, Springer,1997, pp. 432--446.
  • G. Kuper, L. Libkin, and J. Paredaens (editors) Constraint databases, Springer-Verlag,2000.