Non-representable relation algebras from vector spaces

Australasian Journal of Logic 17 (2):82-109 (2020)
  Copy   BIBTEX

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).

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Atom structures of cylindric algebras and relation algebras.Ian Hodkinson - 1997 - Annals of Pure and Applied Logic 89 (2):117-148.
Representations for Small Relation Algebras.Hajnal Andréka & Roger D. Maddux - 1994 - Notre Dame Journal of Formal Logic 35 (4):550-562.

Analytics

Added to PP
2020-04-29

Downloads
5 (#1,344,576)

6 months
1 (#1,042,085)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references