Borel Whitehead Groups
نویسنده
چکیده
We investigate the Whiteheadness of Borel abelian groups (א1-free, without loss of generality as otherwise this is trivial). We show that CH (and even WCH) implies any such abelian group is free, and always א2-free. 1998 Mathematics Subject Classification 03C60, 03E15, 20K20.
منابع مشابه
Test Groups for Whitehead Groups
We consider the question of when the dual of a Whitehead group is a test group for Whitehead groups. This turns out to be equivalent to the question of when the tensor product of two Whitehead groups is Whitehead. We investigate what happens in different models of set theory.
متن کاملFive-value rich lines, Borel directions and uniqueness of meromorphic functions
For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ ...
متن کاملar X iv : 1 30 6 . 12 70 v 1 [ m at h . L O ] 6 J un 2 01 3 UNIVERSAL COUNTABLE BOREL QUASI - ORDERS
In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of Borel reducibility. Following the approach of Louveau and Rosendal for the study of analytic equivalence relations, we study countable Borel qua...
متن کاملA formula for the Whitehead group of a three-dimensional crystallographic group
We give an explicit formula for Whitehead group of a threedimensional crystallographic group Γ in terms of the Whitehead groups of the virtually infinite cyclic subgroups of Γ. 0 Introduction The K-theory of integral group rings of crystallographic groups has been studied by Connolly and Koźniewski [8], Farrell and Hsiang [10], Farrell and Jones [11], Lück and Stamm [15], Quinn [20], Tsapogas [...
متن کاملUniformization and the Diversity of Whitehead Groups
The connections between Whitehead groups and uniformization properties were investigated by the third author in [9]. In particular it was essentially shown there that there is a non-free Whitehead (respectively, א1-coseparable) group of cardinality א1 if and only if there is a ladder system on a stationary subset of ω1 which satisfies 2-uniformization (respectively, ω-uniformization). (See also...
متن کامل