Souslin Trees Which Are Hard to Specialise
نویسنده
چکیده
We construct some +-Souslin trees which cannot be specialised by any forcing which preserves cardinals and coonalities. For a regular cardinal we use the principle, for singular we use squares and diamonds.
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Higher Souslin Trees and the Gch, Revisited
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 ho...
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