Logic and Foundations of Mathematics Commons^™

The Systems Of Post And Post Algebras: A Demonstration Of An Obvious Fact, Daviel Leyva

USF Tampa Graduate Theses and Dissertations

In 1942, Paul C. Rosenbloom put out a definition of a Post algebra after Emil L. Post published a collection of systems of many–valued logic. Post algebras became easier to handle following George Epstein’s alternative definition. As conceived by Rosenbloom, Post algebras were meant to capture the algebraic properties of Post’s systems; this fact was not verified by Rosenbloom nor Epstein and has been assumed by others in the field. In this thesis, the long–awaited demonstration of this oft–asserted assertion is given.

After an elemental history of many–valued logic and a review of basic Classical Propositional Logic, the systems given …