Series: Penn State Logic Seminar

Date: Tuesday, April 20, 2004

Time: 2:30 - 3:45 PM

Place: 307 Boucke Building

Speaker: Japheth Wood, Mathematics, Chatham College

Title: The Typeset of a Variety is Undecidable

  A universal algebra consists of a set and a collection of operations
  on the elements of that set. The typeset of a finite algebra
  classifies the local structure of the algebra, according to which of
  the five possible types occur. This typeset can also give a useful
  description of equationally defined classes of algebras, or
  varieties, according to which types of local structures occur among
  its finite members.  In joint work with R. McKenzie, we proved that
  the typeset of a variety is not recursively computable by
  interpreting the halting problem for Turing machines. This talk will
  give a brief overview of the structure of finite algebras (Tame
  Congruence Theory), and the undecidability proof.