Tarski Algebras Research Articles

Decomposability of free Tarski algebras

In this paper we study the direct decomposability of free Tarski algebras. We show that infinite freely generated Tarski algebras are directly indecomposable, whereas finite freely generated Tarski algebras can only be decomposed into a direct product of two factors, one of which is the two-element Tarski algebra.

Free monadic Tarski algebras

A. Monteiro and L. Iturrioz [7], introduced the notion of monadic Tarski algebras as a generalization of the monadic Boolean algebras considered by P. Halmos [6]. They represent the algebraic version of a fragment of the functional monadic calculus. In this paper we determine the structure of the monadic Tarski algebras with a finite set of free generators.

On dynamic algebras

Dynamic algebras are the Lindenbaum–Tarski algebras of dynamic logics. These algebras can be considered as Boolean algebras with some operators, indexed by the elements of some Kleene algebra. In this paper we prove that there are infinitely many finitely generated varieties of dynamic algebras having undecidable equational theories. All these varieties are generated by representable dynamic algebras.