Borel structures and Borel theories. (English) Zbl 1221.03044

Summary: We show that there is a complete, consistent Borel theory which has no “Borel model” in the following strong sense: There is no structure satisfying the theory for which the elements of the structure are equivalence classes under some Borel equivalence relation and the interpretations of the relations and function symbols are uniformly Borel. We also investigate Borel isomorphisms between Borel structures.


03E15 Descriptive set theory
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[1] Proceedings of the 19th IEEE symposium on Logic in Computer Science pp 110– (2008)
[2] Handbook on set theory pp 297–
[3] Logic Colloquium ’80 (Prague, 1980) 108 pp 147– (1982)
[4] The descriptive set theory of Polish group actions (1996) · Zbl 0949.54052
[5] Classical descriptive set theory 156 (1995) · Zbl 0819.04002
[6] Proceedings of the workshop on effective models of the uncountable, 2009
[7] DOI: 10.1007/BFb0079689
[8] Classical Banach spaces I (1996)
[9] Model-theoretic logics pp 579– (1985)
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