For more information about this meeting, contact Stephen Simpson.

Title: | The logical structure of arithmetic and set theory, part 4 |

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 / 14 / 2008 |

Time: | 02:30pm - 03:45pm |