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 Abstract: 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.