Non-representable relation algebras from vector spaces

  • Ian Hodkinson

Abstract




Extending a construction of Andreka, Givant, and Nemeti (2019), we construct some finite vector spaces and use them to build finite non-representable relation algebras. They are simple, measurable, and persistently finite, and they validate arbitrary finite sets of equations that are valid in the variety RRA of representable relation algebras. It follows that there is no finitely axiomatisable class of relation algebras that contains RRA and validates every equation that is both valid in RRA and preserved by completions of relation algebras. Consequently, the variety generated by the completions of representable relation algebras is not finitely axiomatisable. This answers a question of Maddux (2018).




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Published
2020-04-24
How to Cite
HODKINSON, Ian. Non-representable relation algebras from vector spaces. The Australasian Journal of Logic, [S.l.], v. 17, n. 2, p. 82-109, apr. 2020. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/6467>. Date accessed: 02 july 2020. doi: https://doi.org/10.26686/ajl.v17i2.6467.