Cardinal invariants related to permutation groups

We consider the possible cardinalities of the following three cardinal invariants which are related to the permutation group on the set of natural numbers: ag := the least cardinal number of maximal cofinitary permutation groups; ap := the least cardinal number of maximal almost disjoint permutation families; c(Sym(N)) := the cofinality of the permutation group on the set of natural numbers. We show that it is consistent with ZFC that ap = ag < c(Sym(N)) = 2; in fact we show that in the Miller model ap = ag = 1 < 2 = c(Sym(N)).

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: Bart Kastermans, Yi Zhang 0008
• Keywords: APAL 2006, Cardinal Number, Natural Numbers, Permutation Group