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Logic GroupSchool of Mathematics |
Abstract: I will explain a motivation for Abstract Elementary Classes in terms of building large structures from small ones. The methodology is to translate the definition into category-theoretic language and thereby also give a generalization which also includes abstract metric classes and rather different examples such as profinite groups.
Time: 15:00 17:00 October 29th 2009Abstract: I will explain a motivation for Abstract Elementary Classes in terms of building large structures from small ones. The methodology is to translate the definition into category-theoretic language and thereby also give a generalization which also includes abstract metric classes and rather different examples such as profinite groups.
Time: 16:00 18:00 November 4th 2009Abstract: I will present section 539Q of Fremlin's Measure Theory book introducing his notion of an Exhaustivity Rank and proving the result that every non-measurable Maharam algebra has rank at least the ordinal power $\omega^\omega$.
Time: 16:00 18:00 December 9th 2009Abstract: I will present a modern proof of Hechler theorem about the following consistency result: Let P a partial order Aleph_0 -direct it is consistent with ZFC that there exist a cofinal embedding from P to (omega^omga,<^*); the forcing used will be ccc and of cardinality less then |P|^aleph_0.
Maxim R. Burke: A proof of Hechler's theorem on embedding aleph_1 -directed sets co nally into (omega^omga. =<*), Arch. Math. Logic 36 (1997), pages 399-403.
Time: 16:00 18:00 January 13th 2010Abstract:In recent work with Magidor and Shelah we formulated and proved consistent a forcing axion which applies to the successor of a strong limit singular cardinal kappa of any cofinality. If one starts with a model of SuSiFA and forces with a further Radin forcing, one obtains a model in which the singular cardinal hypothesis fails and the combinatorial properties of kappa^+ are well controlled.
Time: 16:00 18:00 January 20th 2010Abstract: I will present the opening coloring axiom and some of their consequence. In particular I will present the proof that the value of the bounding number is decided in presence of OCA. The proof use the construction of gaps .
Time: 15:00 17:00 March 10th 2010Abstract:
Time: 15:00 17:00 April 28th 2010Abstract: We present a thin tall Booelan algebra which is isomorphic to every one of its uncountable subalgebras.
Time: 15:00 17:00