Small u(κ) at singular κ with compactness at κ
We show that the tree property, stationary reflection and the failure of approachability at κ + + are consistent with u ( κ ) = κ + < 2 κ , where κ is a singular strong limit cardinal with the countable or uncountable cofinality. As a by-product, we show that if λ is a regular cardinal, then stat...
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| Veröffentlicht in: | Archive for mathematical logic 2022-02, Vol.61 (1-2), p.33-54 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We show that the tree property, stationary reflection and the failure of approachability at
κ
+
+
are consistent with
u
(
κ
)
=
κ
+
<
2
κ
, where
κ
is a singular strong limit cardinal with the countable or uncountable cofinality. As a by-product, we show that if
λ
is a regular cardinal, then stationary reflection at
λ
+
is indestructible under all
λ
-cc forcings (out of general interest, we also state a related result for the preservation of club stationary reflection). |
|---|---|
| ISSN: | 0933-5846 1432-0665 |
| DOI: | 10.1007/s00153-021-00776-5 |