Higher Souslin Trees and the Gch, Revisited
نویسنده
چکیده
It is proved that for every uncountable cardinal λ, GCH+ (λ) entails the existence of a cf(λ)-complete λ-Souslin tree. In particular, if GCH holds and there are no א2-Souslin trees, then א2 is weakly compact in Gödel’s constructible universe, improving Gregory’s 1976 lower bound. Furthermore, it follows that if GCH holds and there are no א2 and א3 Souslin trees, then the Axiom of Determinacy holds in L(R).
منابع مشابه
μ-complete Souslin trees on μ+
Introduction The old problem of the existence of Souslin trees has attracted the attention of many (see [Je] for history). While the א1 case is settled, the consistency of GCH + SH(א2) is still an open question. Gregory showed in [G] that GCH + “there is a non reflecting stationary set of ω-cofinal elements of ω2” implies the existence of an א2-Souslin tree. Gregory’s result showed that the con...
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