Starting from a model of ZFC+GCH, iterated forcing is a method of building a new larger model in which (for example) the continuum hypothesis fails and in fact the continuum $c$ (the cardinality of the set R of real numbers) can become arbitrarily large. Several other so called "cardinal characteristics" may be changed as well: for example, the number cov(null) (the smallest size of a family of Lebesgue null sets whose union is all of R) or the similarly defined number cov(meager), where null sets are replaced by meager sets (or equivalently: by closed nowhere dense sets. For example, iterating Cohen's original forcing one can get a model where cov(null) is still small (aleph1), while cov(meager) becomes c (which will be large).
In my talk I will present a method for iterating forcing notions that allows us to selectively increase certain cardinals to prescribed values. In particular, intersecting a forcing notion with elementary submodels of the universe will yield new forcing notions. If the submodels are carefully chosen, then an analysis of the properties of these new forcing notions will allows us to compute the value of certain cardinal characteristics in the generic extension.
To join this webinar, please send an email to r.zoghi@gmail.com.