The number of countable subdirect powers of finite unary algebras

Abstract: The number of subdirect powers of an finite algebraic structure is a question that has appeared at various points in recent history. The situation is known in full for groups, and to some extent in semigroups. We answer the question for unary algebras, and look at how the situation is more complicated for infinite algebras. We then discuss what these results can tell us about the general question, and how it ties into other topics such as boolean separation.

computational complexitycategory theorylogic

Audience: researchers in the topic

PALS Panglobal Algebra and Logic Seminar

Series comments: The PALS seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. Please contact one of the organizers for the Zoom password, to join the mailing list or if you want to speak.