5 papers · 1 filter
Isomorphism types of definable (maximal) cofinitary groups
Lukas Schembecker
Kastermans proved that consistently has a cofinitary representation. We present a short proof that alway…
Realizing arbitrarily large spectra of
Vera Fischer, Lukas Schembecker
We improve the state-of-the-art proof techniques for realizing various spectra of in order to realize arbitrarily large spectra. Thus, we make significant…
Universally Sacks-indestructible combinatorial families of reals
Vera Fischer, Lukas Schembecker
We introduce the notion of an arithmetical type of combinatorial family of reals, which serves to generalize different types of families such as mad families, maximal cofinitary gr…
Cofinitary groups and projective well-orders
Vera Fischer, Lukas Schembecker, David Schrittesser
We introduce the notion of a tight cofinitary group, which captures forcing indestructibility of maximal cofinitary groups for a long list of partial orders, including Cohen, Sacks…
Partitions of Baire space into compact sets
Vera Fischer, Lukas Schembecker
Under we construct a partition of Baire space into compact sets, which is indestructible by countably supported iteration and product of Sacks forcing of any length, an…