Logic Seminar Abstracts |
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Title: Martin's Maximum and limitations on presaturated towers Speaker: Sean Cox Affiliation: Universität Münster Time: 3pm, Wednesday, September 21 Location: Math 220 Abstract: Woodin devised several examples of "stationary tower forcings" which, in the presence of Woodin cardinals in V, give rise to "generic almost huge" embeddings: if G is generic for the tower then in V[G] there is a map j:V &rarr N where j can have a small critical point (like ω1 or ω2) and N is closed under < j(crit(j)) sequences from V[G]. These posets are instances of the more general notion of forcing with a tower of ideals. A tower of ideals is called presaturated if (roughly) it gives rise to a generic almost huge embedding. In this talk I will discuss some joint work with Matteo Viale about the limitations that strong forcing axioms (like Martin's Maximum) place on the existence of presaturated towers. This work echoes some earlier results by Foreman-Magidor and Burke. |
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