Principal and Boolean Congruences on $$\varvec{IKt}$$ IKt -Algebras

Studia Logica 106 (4):857-882 (2018)
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Abstract

The IKt-algebras were introduced in the paper An algebraic axiomatization of the Ewald’s intuitionistic tense logic by the first and third author. In this paper, our main interest is to investigate the principal and Boolean congruences on IKt-algebras. In order to do this we take into account a topological duality for these algebras obtained in Figallo et al. :673–701, 2017). Furthermore, we characterize Boolean and principal IKt-congruences and we show that Boolean IKt-congruence are principal IKt-congruences. Also, bearing in mind the above results, we obtain that Boolean IKt-congruences are commutative, regular and uniform. Finally, we characterize the principal IKt-congruences in the case that the IKt-algebra is linear and complete whose prime filters are complete and also the case that it is linear and finite. This allowed us to establish that the intersection of two principal IKt-congruences on these algebras is a principal one and also to determine necessary and sufficient conditions so that a principal IKt-congruence is a Boolean one on theses algebras.

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References found in this work

Intuitionistic tense and modal logic.W. B. Ewald - 1986 - Journal of Symbolic Logic 51 (1):166-179.
Distributive Lattices.Raymond Balbes & Philip Dwinger - 1977 - Journal of Symbolic Logic 42 (4):587-588.
Tense operators on De Morgan algebras.A. V. Figallo & G. Pelaitay - 2014 - Logic Journal of the IGPL 22 (2):255-267.

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