Egrot, ROB;
Hirsch, ROBIN;
(2021)
FIRST-ORDER AXIOMATISATIONS of REPRESENTABLE RELATION ALGEBRAS NEED FORMULAS of UNBOUNDED QUANTIFIER DEPTH.
Journal of Symbolic Logic
10.1017/jsl.2021.88.
(In press).
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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.
| Type: | Article |
|---|---|
| Title: | FIRST-ORDER AXIOMATISATIONS of REPRESENTABLE RELATION ALGEBRAS NEED FORMULAS of UNBOUNDED QUANTIFIER DEPTH |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jsl.2021.88 |
| Publisher version: | https://doi.org/10.1017/jsl.2021.88 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10139073 |
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