Varietes of tense algebras

• Autorzy: Kowalski T.
• Języki publikacji: EN

Abstrakty

EN

The paper has two parts preceded by quite comprehensive preliminaries. In the first part it is shown that a subvariety of the variety T of all tense algebras is discriminator if and only if it is semisimple. The variety T turns out to be the join of an increasing chain of varieties Dn, which are discriminator varieties. The argument carries over to all finite type varieties of boolean algebras with operators satysfying some term conditions. In the case of tense algebras, the varieties Dn can be further characterised by certain natural conditions on Kripke frames. In the second part it is shown that the lattice of subvarieties of Do has two atoms, the lattice of subvarieties of D1 has countably many atoms, and for n>1, the lattice of subvarieties of Dn has continuum atoms. The proof of the second of the above statements involves a rather detailed description of zero-generated simple algebras in D1. Almost all the arguments are cast in algebraic form, but both parts begin with an outline describing their contents from the dualpoints of view of tense logics.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 1998
• Tom: No. 32
• Strony: 53--95

Twórcy

autor

Kowalski T.

• Uniwersytet Jagielloński Katedra Logiki ul. Grodzka 52 31-044 Kraków,