Abstract
We prove that modal definability with respect to the class of all structures with two commuting equivalence relations is an undecidable problem. The construction used in the proof shows that the same is true for the subclass of all finite structures. For that reason we prove that the first-order theories of these classes are undecidable and reduce the latter problem to the former.
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Yana Rumenova is the winner of the Ivan Soskov Logic Prize 2021 (Bulgaria) and contestant in the 2nd World Logic Prizes Contest, UNILOG’2022, Crete.
Tinko Tinchev is supported by contract DN 02-15/19.12.2016 with Bulgarian Science Fund.
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Rumenova, Y., Tinchev, T. Modal Definability: Two Commuting Equivalence Relations. Log. Univers. 16, 177–194 (2022). https://doi.org/10.1007/s11787-022-00299-4
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DOI: https://doi.org/10.1007/s11787-022-00299-4
Keywords
- Correspondence theory
- Modal definability
- Commuting equivalence relations
- Undecidability
- Relative elementary definability