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- Title
FIRST-ORDER AXIOMATISATIONS OF REPRESENTABLE RELATION ALGEBRAS NEED FORMULAS OF UNBOUNDED QUANTIFIER DEPTH.
- Authors
EGROT, ROB; HIRSCH, ROBIN
- Abstract
Using a variation of the rainbow construction and various pebble and colouring games, we prove that RRA, the class of all representable relation algebras, cannot be axiomatised by any first-order relation algebra theory of bounded quantifier depth. We also prove that the class At(RRA) of atom structures of representable, atomic relation algebras cannot be defined by any set of sentences in the language of RA atom structures that uses only a finite number of variables.
- Subjects
RELATION algebras; MATROIDS; PEBBLES; RAINBOWS; RAYLEIGH number
- Publication
Journal of Symbolic Logic, 2022, Vol 87, Issue 3, p1283
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2021.88