منابع مشابه
On full Souslin trees
In the present note we answer a question of Kunen (15.13 in [Mi91]) showing (in 1.7) that it is consistent that there are full Souslin trees. ∗ We thank the NSF for partially supporting this research under grant #144-EF67. Publication No 624.
متن کاملSouslin Trees and Degrees of Constructibility
This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we use this characterization to realize any constructible dual algebraic lattice as a possible initial segment of the degrees of constructibility. In a s...
متن کاملSouslin trees and successors of singular cardinals
The questions concerning existence of Aronszajn and Souslin trees are of the oldest and most dealt-with in modern set theory. There are many results about existence of h+-Aronszajn trees for regular cardinals A. For these cases the answer is quite complete. (See Jech [6] and Kanamory & Magidor [8] for details.) The situation is quite different when A is a singular cardinal. There are very few r...
متن کاملHigher 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...
متن کاملMore on Almost Souslin Kurepa Trees
It is consistent that there exists a Souslin tree T such that after forcing with it, T becomes an almost Souslin Kurepa tree. This answers a question of Zakrzewski [6].
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1987-0891159-4