Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 77, Issue 4 (2012), 1211-1244.
Undecidability of representability as binary relations
In this article we establish the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures. In particular, representability and finite representability are undecidable for Boolean monoids and lattice ordered monoids, while representability is undecidable for Jónsson's relation algebra. We also establish a number of undecidability results for representability as algebras of injective functions.
J. Symbolic Logic, Volume 77, Issue 4 (2012), 1211-1244.
First available in Project Euclid: 15 October 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03G15: Cylindric and polyadic algebras; relation algebras 20M30: Representation of semigroups; actions of semigroups on sets
Secondary: 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 08A99: None of the above, but in this section
Hirsch, Robin; Jackson, Marcel. Undecidability of representability as binary relations. J. Symbolic Logic 77 (2012), no. 4, 1211--1244. doi:10.2178/jsl.7704090. https://projecteuclid.org/euclid.jsl/1350315584