datum: 23.10.2019 v 16:00
název: Profiniteness and finitely generated varieties
přednášející: Michał Stronkowski (Warsaw University of Technology)
místo konání: UI, 2.patro, místnost č.318

souhrn: Profinite algebras are exactly those that are isomorphic to inverse limits of finite algebras. Such algebras are naturally equipped with Boolean topologies. A variety V of algebras is standard if every Boolean topological algebra with the algebraic reduct in V is profinite. We show that there is no algorithm that takes as input a finite algebra A (of a finite type) and decides whether the variety generated by A is standard. We also show the undecidability of some related properties. In particular, we solve the problem posed by Clark, Davey, Freese, and Jackson about finitely determined syntactic congruences in finitely generated varieties. Our work is based on Moore's theorem about undecidability of having definable principal subcongruences for finitely generated varieties. Joint work with Anvar M. Nurakunov.