Choice-Free Duality for Tarski Algebras

Abstract

In [N. Bezhanishvili and W. H. Holliday. Choice-free Stone duality. J. Symb. Log., 85(1):109–148, 2020.], the authors develop a choice-free topological duality for the algebraic category of Boolean algebras. We adapt the techniques and constructions given by Bezhanishvili and Holliday to develop a topological duality for the algebraic category of Tarski algebras without using the Axiom of Choice. Then, we show that the duality presented here for Tarski algebras is in fact a generalization of the duality given by Bezhanishvili and Holliday for Boolean algebras. We also obtain a choice-free topological duality for the algebraic category of generalized Boolean algebra.