Notions Of Density That Imply Representability In Algebraic Logic (1998)
| Citations: | 4 - 1 self |
BibTeX
@MISC{Andréka98notionsof,
author = {Hajnal Andréka and Hajnal Andr Eka and Steven Givant and ISTVAN NEMETI and SZABOLCS MIKULAS and Istv An and N Emeti and ANDRAS SIMON and As Simon},
title = {Notions Of Density That Imply Representability In Algebraic Logic},
year = {1998}
}
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Abstract
. Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable (as a cylindric set algebra) . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin-Monk-Tarski [1985]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of op. cit. mentioned above are special cases of our general theorems. We point out an error in the proof of the Henkin-Monk-Tarski representation theorem for atomic equality-free quasi-polyadic algebras with rectangular atoms. The er...
