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The Lattice of Definability. Origins, Recent Developments, and Further Directions

  • Alexei Semenov
  • Sergey Soprunov
  • Vladimir Uspensky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8476)

Abstract

The paper presents recent results and open problems on classes of definable relations (definability spaces, reducts, relational algebras) as well as sources for the research starting from the XIX century. Finiteness conditions are investigated, including quantifier alternation depth and number of arguments width. The infinite lattice of definability for integers with a successor function (a non ω-categorical structure) is described. Methods of investigation include study of automorphism groups of elementary extensions of structures under consideration, using Svenonius theorem and a generalization of it.

Keywords

Definability definability space reducts Svenonius theorem quantifier elimination decidability automorphisms 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alexei Semenov
    • 1
    • 2
    • 3
  • Sergey Soprunov
    • 2
  • Vladimir Uspensky
    • 1
  1. 1.Moscow State UniversityRussia
  2. 2.Dorodnicyn Computing CenterThe Russian Academy of SciencesRussia
  3. 3.Moscow Pedagogical State UniversityRussia

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