Universal-existential sentences in the simple theory of types (slides)

Abstract: I will talk about ongoing research that is being done in collaboration with Anuj Dawar and Thomas Forster. The simple theory of types (TST) is a simplification, proposed independently by Ramsey and Chwistek, of the underlying system used in Russell and Whiteheadâ€™s Principia. This theory apparently avoids the set theoretic paradoxes by partitioning the universe into types and only allowing sets at a given successor type to contain objects from the preceding type. It has been conjectured that TST decides every universal-existential sentence. In this talk I will show that every existential-universal sentence that is true in some model of TST is true in all models of TST minus infinity that are generated by a sufficiently large finite number of atoms. The talk will continue with a sketch of a proof which shows that TST decides a subclass of the universal-existential sentences. Finally, I will discuss a connection between the universal-existential sentences of TST and the term model of a weakening of the theory of simple types.

To get to campus, take the train from Birmingham New Street to the University stop (7 minutes).

School of Mathematics

University of Birmingham

http://web.mat.bham.ac.uk/R.W.Kaye/

Dr Walter Dean

Department of Philosophy

University of Warwick

http://go.warwick.ac.uk/whdean