Uniformity of the Meager Ideal and Maximal Cofinitary Groups
نویسندگان
چکیده
منابع مشابه
Uniformity of the Meager Ideal and Maximal Coonitary Groups
We prove that every maximal coonitary group has size at least the cardinality of the smallest non{meager set of reals. We also provide a consistency result saying that the spectrum of possible cardinalities of maximal coonitary groups may be quite arbitrary.
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Let κ be an arbitrary regular infinite cardinal and let C denote the set of κ-maximal cofinitary groups. We show that if GCH holds and C is a closed set of cardinals such that 1. κ ∈ C, ∀ν ∈ C(ν ≥ κ), 2. if |C| ≥ κ then [κ, |C|] ⊆ C, 3. ∀ν ∈ C(cof(ν) ≤ κ→ ν ∈ C), then there is a generic extension in which cofinalities have not been changed and such that C = {|G| : G ∈ C}. The theorem generalize...
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In [2], Jörg Brendle used Hechler’s forcing notion for adding a maximal almost family along an appropriate template forcing construction to show that a (the minimal size of a maximal almost disjoint family) can be of countable cofinality. The main result of the present paper is that ag, the minimal size of maximal cofinitary group, can be of countable cofinality. To prove this we define a natur...
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A group G Sym(N) is cofinitary if g has finitely many fixed points for every g ∈G except the identity element. In this paper, we discuss the definability of maximal cofinitary groups and some related structures. More precisely, we show the following two results: (1) Assuming V = L, there is a Π1 1 set of permutations on N which generates a maximal cofinitary group. (2) Assuming V = L, there is ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8396