CONSTRUCTING MAXIMAL COFINITARY GROUPS
نویسندگان
چکیده
Abstract Improving and clarifying a construction of Horowitz Shelah, we show how to construct (in $\mathsf {ZF}$ , i.e., without using the Axiom Choice) maximal cofinitary groups. Among groups construct, one is definable by formula in second-order arithmetic with only few natural number quantifiers.
منابع مشابه
Definable Maximal Cofinitary Groups
Using countable support iteration of S-proper posets, for some appropriate stationary set S, we obtain a generic extension of the constructible universe, in which b = c = א2 and there is a maximal cofinitary group with a Π2-definable set of generators.
متن کاملMaximal cofinitary groups revisited
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...
متن کاملTemplate iterations and maximal cofinitary groups
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...
متن کاملDefinable sets of generators in maximal cofinitary groups
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 ...
متن کاملConstructing maximal subgroups of classical groups
In this paper we show how to construct the maximal subgroups of the finite classical groups of linear, symplectic or unitary type in low-degree
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2023
ISSN: ['0027-7630', '2152-6842']
DOI: https://doi.org/10.1017/nmj.2022.46