A note on a subvariety of linear tense algebras

Mathematical Logic Quarterly 51 (1):104-108 (2005)
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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 paper we consider the subvariety [MATHEMATICAL SCRIPT CAPITAL V] generated by the finite members of Disc. We prove that V is locally finite and we determine its lattice of subvarieties. We also prove that [MATHEMATICAL SCRIPT CAPITAL V] = Disc ∩ Dens = Disc ∩ Cont

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10.1002/malq.200410012

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