### Mathematical logic seminar - September 25, 2007

 Time: 12:00 - 13:20 Room: Scaife Hall 219 Speaker: Rick Statman    Department of Mathematical Sciences Carnegie Mellon University Title: Cartesian monoids. Abstract: Functional programming and equational specification have their roots in the ideas of Herbrand, Godel, Church, Curry and Kleene carried up to the present. The standard was articulated by Backus in his 1978 Turing award lecture: "... a small framework which accommodates a great variety of powerful features entirely as changeable parts." The notion of a Cartesian monoid is a very simple framework. We will see that it accommodates a great variety of powerful features as changeable parts. The six steps: Begin with a "Cantor algebra"; a set together a with surjective pairing function. Add a monoid of functions to the Cantor algebra. Write down the axioms of a Cartesian monoid and construct the free model. Contemplate the "op" of the free model; the piecewise shift operators. Allow an undefined element; partial piecewise shift operators. Consider the algebraic elements. and we arrive at the promised land of $L_{\omega_1^{CK}}$