PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephen Simpson.

Title:The logical structure of arithmetic and set theory, part 3
Seminar:Logic Seminar
Speaker:Stephen G. Simpson, Pennsylvania State University
Abstract:
Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics as a whole. This talk is an elementary introduction to foundations of mathematics. All of the axioms in question are written as sentences in the predicate calculus. In part 1 of the talk, we introduce the axioms of first-order arithmetic, Z_1, a.k.a., Peano Arithmetic, PA. We point out a sense in which the axioms of Z_1 are "practically complete" despite the famous Incompleteness Theorems of Goedel. In part 2 of the talk, we introduce the language and axioms of set theory, a.k.a., ZFC. The language of ZFC is extremely limited, consisting of only one binary predicate which denotes the membership relation. In order to improve the readability of our sentences, we employ a powerful technique known as "definitional extension." As in the case of Z_1, it is found that the axioms of ZFC are "practically complete" despite famous results such as the independence of the Continuum Hypothesis. An important aspect of the ZFC axioms is that they are commonly viewed as the formal axiomatic framework for all of mathematics.

Room Reservation Information

Room Number:MB106
Date:10 / 07 / 2008
Time:02:30pm - 03:45pm