Ruprecht-Karls-Universität Heidelberg
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„The Current State of the Foundations of Set Theory“
Prof. Sy-David Friedman, Universität Wien

Set-theorists have for many years had a pretty good system of axioms for mathematics, the ZFC axioms. But Goedel's incompleteness theorem tells us that no system of axioms, not even ZFC, is complete: there always are statements that can be neither proved nor disproved in any formal system. The most famous example for ZFC is Cantor's continuum hypothesis (CH), stating that any two uncountable sets of real numbers have the same cardinality. Is the incompleteness of ZFC relevant for mathematics? There is evidence for a positive answer, but some will regard the known examples as disguised versions of questions in abstract set theory, lying outside of "core mathematics". Whether the mathematicians of the future will need axioms beyond ZFC to resolve questions at the heart of mathematics remains a fascinating open question. There is no doubt that set-theorists themselves must go beyond ZFC if they wish to resolve questions at the heart of set theory. But before adopting a new axiom it is important to provide evidence for its "truth". Currently such evidence is based on a proposed axiom's value for the development of set theory as mathematics, for the resolution of incompleteness in other areas of mathematics or for a deeper understanding of the set concept. I am optimistsic that there are axioms which possess all three forms of evidence and which will ultimately lead to a resolution of important problems of set theory that are undecided by ZFC alone.

Donnerstag, den 21. Mai 2015 um 17 Uhr c.t. Uhr, in INF 288, HS2 Donnerstag, den 21. Mai 2015 at 17 Uhr c.t., in INF 288, HS2

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Wienhard / Dr. Peon-Nieto