The principle Diamond Star
Mittwoch, 17.4.13, 16:30-17:30, Raum 404, Eckerstr. 1
Pseudoräume
Mittwoch, 24.4.13, 16:30-17:30, Raum 404, Eckerstr. 1
Sonntag, 5.5.13, 00:00-01:00, Hörsaal II, Albertstr. 23b
The pseudointersection number and the tower number
Mittwoch, 8.5.13, 16:30-17:30, Raum 404, Eckerstr. 1
Mittwoch, 15.5.13, 16:30-17:30, Raum 404, Eckerstr. 1
Unsound ordinals
Mittwoch, 15.5.13, 16:30-17:30, Raum 404, Eckerstr. 1
An ordinal zeta is unsound if there are subsets An (n in omega) of it such that as b ranges through the subsets of omega, uncountably many ordertypes are realised by\nthe sets $\bbigcup{n \bin b} An\(.\n\nWoodin in 1982 raised the question whether unsound ordinals\nordinals exist; the answer I found then (to be found in a paper\npublished in the Mathematical Proceedings of the Cambridge Philosophical Society volume 96 (1984) pages 391--411) is this:\n\n\nAssume DC. Then the following are equivalent:\n\ni) the ordinal \)\bomega1^{\bomega + 2}$ (ordinal exponentiation) is unsound\n\nii) there is an uncountable well-ordered set of reals\n\nThat implies that if omega1 is regular and the ordinal mentioned in i) is sound, then omega1 is strongly inaccessible in the constructible universe. Under DC, every\nordinal strictly less than the ordinal mentioned in i) is sound.\n\n\nThere are many open questions in this area: in particular, in\nSolovay's famous model where all sets of reals are Lebesgue measurable,\nis every ordinal sound ? The question may be delicate, as Kechris and Woodin have shown that if the Axiom of Determinacy is true then there\nis an unsound ordinal less than omega_2.\n\n
Resurrecting Ramsey ultrafilters
Mittwoch, 29.5.13, 16:30-17:30, Raum 404, Eckerstr. 1
Generalized random forcing for weakly compact
Mittwoch, 5.6.13, 16:30-17:30, Raum 404, Eckerstr. 1
On Limitations of the Ehrenfeucht-Fraïssé method
Mittwoch, 12.6.13, 16:30-17:30, Raum 404, Eckerstr. 1
Heyting algebras
Mittwoch, 19.6.13, 16:30-17:30, Raum 404, Eckerstr. 1
Inner Models for Set Theory Defined by Generalized Logics
Mittwoch, 26.6.13, 16:30-17:30, Raum 404, Eckerstr. 1
A category-theoretic viewpoint on first definitions in general topology
Mittwoch, 3.7.13, 16:30-17:30, Raum 404, Eckerstr. 1
We observe that several definitions in a first course on general topology, such as Hausdorff,\ndense, T0, T1, admit an easy reformulation as computations with partial preorders of\ncategory-theoretic nature. Namely, these computations correspond to rules for manipulating\ncommutative diagrams involving only finite topological spaces as constants (and variables). We\nsuggest a calculus based on these rules.\n\n
The real field with dense subgroups of the torus
Mittwoch, 10.7.13, 16:30-17:30, Raum 404, Eckerstr. 1