# Whitehead groups may be not free, even assuming CH, I

@article{Shelah1977WhiteheadGM,
title={Whitehead groups may be not free, even assuming CH, I},
author={Saharon Shelah},
journal={Israel Journal of Mathematics},
year={1977},
volume={28},
pages={193-204}
}
• S. Shelah
• Published 1977
• Mathematics
• Israel Journal of Mathematics
AbstractWe prove the consistency with ZFC+G.C.H. of an assertion, which implies several consequences of $$MA + 2^{\aleph _0 } > \aleph _1$$ , which $$\diamondsuit \aleph _1$$ implies their negation.
Whitehead groups may not be free even assuming ch, II
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• Mathematics
• 1978
We present here a (weak) axiom which implies some of the consequences of MA, but is consistent with GCH. We use the method of Jensen in his proof of consis (ZFC+GCH+SH).
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• Mathematics, Computer Science
• Ann. Pure Appl. Log.
• 2010
Abstract We show that it is consistent with ordinary set theory Z F C and the generalized continuum hypothesis that there exist two ℵ 1 -separable abelian groups of cardinality ℵ 1 which areExpand
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• Mathematics
• 1992
Techniques of uniformization are used to prove that it is not consistent that the Whitehead groups of cardinality ℵ1 are exactly the strongly ℵ1-free groups. Some consequences of the assumption thatExpand
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For abelian groups, ifV=L, Ext(G, Z) cannot have cardinality ℵ0. We show that G.C.H. does not imply this. See Hiller and Shelah [2], Hiller, Huber and Shelah [3], Nunke [5] and Shelah [6, 7, 8] forExpand
The monadic theory of (ω2, <) may be complicated
• Mathematics, Computer Science
• Arch. Math. Log.
• 1992
SummaryAssume ZFC is consistent then for everyB⫅ω there is a generic extension of the ground world whereB is recursive in the monadic theory ofω2.
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We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\omega_1$ and $-\omega_1$, answering a question of J. Baumgartner.Expand
The uniformization property for ℵ2
• Mathematics
• 1980
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Iterated souslin forcing, the principles ⋄(E) and a generalisation of the axiom SAD
AbstractThe axiom SAD was introduced in our paper with Avraham and Shelah [1]. It is a Martin’s Axiom type of principle, having some of the consequences of MA plus $$2^{\aleph _0 } > \aleph _1$$ ,Expand

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