Atoms in infinite dimensional free sequence-set algebras

A. Tarski proved that the m-generated free algebra of $\mathrm{CA}_{\alpha}$, the class of cylindric algebras of dimension $\alpha$, contains exactly $2^m$ zero-dimensional atoms, when $m\ge 1$ is a finite cardinal and $\alpha$ is an arbitrary ordinal. He conjectured that, when $\alpha$ is infinite, there are no more atoms. This conjecture has not been confirmed or denied yet. In this article, we show that Tarski's conjecture is true if $\mathrm{CA}_{\alpha}$ is replaced by $\mathrm{D}_{\alpha}$, $\mathrm{G}_{\alpha}$, but the $m$-generated free $\mathrm{Crs}_{\alpha}$ algebra is atomless

On Logical Analysis of Relativity Theories

The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.Comment: 19 pages, 1 figure

Term algebras of elementarily equivalent atom structures

We exhibit two relation algebra atom structures such that they are elementarily equivalent but their term algebras are not. This answers Problem 14.19 in Hirsch and Hodkinson’s text Relation Algebras by Games. © 2018, Springer Nature Switzerland AG