2015 SMAS Dean's Scholar Enrichment Seminar
The inaugural talk was given by Professor Martin Bunder. Martin has been on the Wollongong Maths staff, on a paid or honorary capacity since 1969. He has been an active researcher in the fields of Formal Logic, Set Theory, and Foundations of Mathematics and Number Theory as well as some other areas. Receiving his PhD from the University of Amsterdam in 1969, Martin has authored around 150 papers. He is also "related" to two of the mathematicians mentioned in this talk, Haskell Curry was his PhD supervisor, David Hilbert Curry's supervisor.
The slides were prepared by his daughter Rachel, a Wollongong Maths Honours graduate, from Martin's handwritten version.
A History of Set Theory
Set Theory was first developed by Cantor in 1874. Much of this material was described by Frege, using a basis of Logic in 1879 and 1903. This Set Theory required only two simple and intuitively satisfying axioms, which allowed the proofs of many results as well as the definition of natural numbers, from which most arithmetical properties followed. Unfortunately the simple axioms led to inconsistency, i.e. the proof of contradictory statements. These are called the set theoretic paradoxes.
The talk will outline the early “naïve” set theory, some of its applications as well as some of the paradoxes and some of the methods that have been used to avoid them.