Kurt Gödel Research Center

2012 seminar talk: Separation of regularity properties

Talk held by Giorgio Laguzzi (KGRC) at the KGRC seminar on 2012-03-15.

Abstract

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 2^nd 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.