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- W2801036769 abstract "Abstract Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing that any of their eight Boolean combinations can be forced to hold at ${kappa ^{ + + }}$ , assuming that $kappa = {kappa ^{ < kappa }}$ and there is a weakly compact cardinal above κ . If in addition κ is supercompact then we can force κ to be ${aleph _omega }$ in the extension. The proofs combine the techniques of adding and then destroying a nonreflecting stationary set or a ${kappa ^{ + + }}$ -Souslin tree, variants of Mitchell’s forcing to obtain the tree property, together with the Prikry-collapse poset for turning a large cardinal into ${aleph _omega }$ ." @default.
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- W2801036769 date "2018-03-01" @default.
- W2801036769 modified "2023-10-16" @default.
- W2801036769 title "THE EIGHTFOLD WAY" @default.
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- W2801036769 doi "https://doi.org/10.1017/jsl.2017.69" @default.
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