- Tytuł:
- Strong covering without squares
- Autorzy:
- Shelah, Saharon
- Powiązania:
- https://bibliotekanauki.pl/articles/1204997.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
set theory
covering
strong covering lemma
pcf theory - Opis:
-
Let W be an inner model of ZFC. Let κ be a cardinal in V. We say that κ-covering holds between V and W iff for all X ∈ V with X ⊆ ON and V ⊨ |X| < κ, there exists Y ∈ W such that X ⊆ Y ⊆ ON and V ⊨ |Y| < κ. Strong κ-covering holds between V and W iff for every structure M ∈ V for some countable first-order language whose underlying set is some ordinal λ, and every X ∈ V with X ⊆ λ and V ⊨ |X| < κ, there is Y ∈ W such that X ⊆ Y ≺ M and V ⊨ |Y| < κ.
We prove that if κ is V-regular, $κ^+_V = κ^+_W$, and we have both κ-covering and $κ^+$-covering between W and V, then strong κ-covering holds. Next we show that we can drop the assumption of $κ^+$-covering at the expense of assuming some more absoluteness of cardinals and cofinalities between W and V, and that we can drop the assumption that $κ^+_W = κ^+_V$ and weaken the $κ^+$-covering assumption at the expense of assuming some structural facts about W (the existence of certain square sequences). - Źródło:
-
Fundamenta Mathematicae; 2000, 166, 1-2; 87-107
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł