Series: Penn State Logic Seminar Date: Tuesday, May 17, 2005 Time: 2:30 - 3:45 PM Place: 123 Pond Laboratory Speaker: Stephen G. Simpson, Penn State, Mathematics Title: A Slick Proof of the Unsolvability of the Word Problem for Groups Abstract: A famous theorem of P. Novikov 1955 and W. W. Boone 1959 asserts the existence of a finitely presented group with unsolvable word problem. In my Spring 2005 topics course (MATH 574, Topics in Mathematical Logic), I presented Boone's proof, as simplified by J. L. Britton, 1963. In this seminar I shall present a truly slick, streamlined proof, due to S. Aanderaa and D. E. Cohen, 1980. Instead of Turing machines or register machines, the Aanderaa/Cohen proof uses another kind of machines, called modular machines, which I shall discuss in detail. In addition, the Aanderaa/Cohen proof uses Britton's Lemma. I shall omit the proof of Britton's Lemma, which can be found in my course notes at http://www.personal.psu.edu/t20/notes/.