Maximal cofinitary groups revisited |
| |
Authors: | Vera Fischer |
| |
Institution: | Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna, Austria |
| |
Abstract: | Let κ be an arbitrary regular infinite cardinal and let denote the set of κ‐maximal cofinitary groups. We show that if holds and C is a closed set of cardinals such that then there is a generic extension in which cofinalities have not been changed and such that . The theorem generalizes a result of Brendle, Spinas and Zhang (cf. 4 ) regarding the possible sizes of maximal cofinitary groups. Our techniques easily modify to provide analogous results for the spectra of maximal κ‐almost disjoint families in , maximal families of κ‐almost disjoint permutations on κ and maximal families of κ‐almost disjoint functions in . In addition we construct a κ‐Cohen indestructible κ‐maximal cofinitary group and so establish the consistency of , which for is due to Yi Zhang (cf. 10 ). |
| |
Keywords: | |
|
|