Heike Mildenberger :
On Shoenfield's Absoluteness Theorem
Time and place
Thursday, 4.12.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Abstract
In 1961, Joseph R. Shoenfield (1927 - 2000) proved the following theorem, that later has been called Shoenfield's Absoluteness Theorem:\n\nEvery Sigma^12(a) relation and every Pi^12(a) relation is absolute for all inner models M of the Zermelo-Fraenkel axioms and dependent choice that contain the real number a as an element.\n\nThe notions will be explained. On our way towards a sketch of proof we will encounter computable reals (same as in computer science and in numerical mathematics), arithmetical properties (same as in algebra and in number theory), provability (same all over classical mathematics), and Borel sets (same as in measure theory and in probability theory). Absoluteness of a relation, and in particular absoluteness of truth of a statement, is a useful property. The axiomatic background, Zermelo-Fraenkel and dependent choice, is much weaker than the axiomatic basis, e.g., for Linear Algebra 1.\n