We present two ways in which the model L(R) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing;… (More)

There is a proper Baire category preserving forcing which adds infinitely equal real but no Cohen real. This resolves a long-standing open problem of David Fremlin. The forcing has a natural… (More)

We show that in the presence of large cardinals proper forcings do not change the theory of L(R) with real and ordinal parameters and do not code any set of ordinals into the reals unless that set… (More)

We isolate a forcing which increases the value of δ 2 while preserving ω1 under the assumption that there is a precipitous ideal on ω1 and a measurable cardinal.

We define the property of Π2-compactness of a statement φ of set theory, meaning roughly that the hard core of the impact of φ on combinatorics of א1 can be isolated in a canonical model for the… (More)

In the context of arbitrary Polish groups, we investigate the Galvin– Mycielski–Solovay characterization of strong measure zero sets as those sets for which a meager collection of right translates… (More)