2012 seminar talk: Separation of regularity properties
Talk held by Giorgio Laguzzi (KGRC) at the KGRC seminar on 2012-03-15.
The talk centers around the separation of different regularity properties of sets of reals, topic which I deal with in my PhD thesis under the supervision of Sy Friedman. The notion of regularity will be presented in a rather general way; the approach will be slightly different (but practically equivalent) from Yurii Khomskii's one. Results of separation will include statements regarding the 2nd level of projective hierarchy and statements about the full family of all sets of reals. The main result of the talk will be the construction of a model where every set of reals is Silver-regular, but there exists a non-Miller-regular set, for which Shelah's amalgamation will be essential.