Bulletin of Symbolic Logic

Erdős graphs resolve Fine’s canonicity problem

Robert Goldblatt, Ian Hodkinson, and Yde Venema

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We show that there exist 20 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation results of Thomason). The constructions use the result of Erdős that there are finite graphs with arbitrarily large chromatic number and girth.

Article information

Source
Bull. Symbolic Logic, Volume 10, Issue 2 (2004), 186-208.

Dates
First available in Project Euclid: 26 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1082986262

Digital Object Identifier
doi:10.2178/bsl/1082986262

Mathematical Reviews number (MathSciNet)
MR2062417

Zentralblatt MATH identifier
1060.03038

Keywords
Boolean algebras with operators modal logic random graphs canonical extension elementary class variety

Citation

Goldblatt, Robert; Hodkinson, Ian; Venema, Yde. Erdős graphs resolve Fine’s canonicity problem. Bull. Symbolic Logic 10 (2004), no. 2, 186--208. doi:10.2178/bsl/1082986262. https://projecteuclid.org/euclid.bsl/1082986262


Export citation