## Abstract In [1], Bull gave completeness proofs for three axiom systems with respect to tense logic with time linear and rational, real and integral. The associated varieties, Dens, Cont and Disc, are generated by algebras with frames {ℚ, <, >}, {ℝ, <, >} and {ℤ, <, >}, respectively. In this pape
On subvarieties of symmetric closure algebras
✍ Scribed by J.P. Dı́az Varela
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 163 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0168-0072
No coin nor oath required. For personal study only.
✦ Synopsis
The aim of this paper is to investigate the variety of symmetric closure algebras, that is, closure algebras endowed with a De Morgan operator. Some general properties are derived. Particularly, the lattice of subvarieties of the subvariety of monadic symmetric algebras is described and an equational basis for each subvariety is given.
📜 SIMILAR VOLUMES
Let X be a δ-variety over some δ-field . Denote by td δ X/ , or simply td δ X if the ground field is understood, the δ-transcendental degree of X over . Suppose td δ X = d; Johnson [Comment. Math. Helv. 44 (1969), 207-216] showed that there is an increasing chain of δ-subvarieties of length ωd in X.
## Abstract A theorem of Birkhoff‐Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many‐sorted sets, i.e., indexed families of sets, such a theorem is not longer