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. © 2014 Springer International Publishing Switzerland.
CITATION STYLE
Semenov, A., Soprunov, S., & Uspensky, V. (2014). The lattice of definability. Origins, recent developments, and further directions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8476 LNCS, pp. 23–38). Springer Verlag. https://doi.org/10.1007/978-3-319-06686-8_3
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