117 research outputs found
Atoms in infinite dimensional free sequence-set algebras
A. Tarski proved that the m-generated free algebra of ,
the class of cylindric algebras of dimension , contains exactly
zero-dimensional atoms, when is a finite cardinal and is an
arbitrary ordinal. He conjectured that, when 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 is
replaced by , , but the -generated
free algebra is atomless
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