- Tytuł:
- More set-theory around the weak Freese–Nation property
- Autorzy:
-
Fuchino, Sakaé
Soukup, Lajos - Powiązania:
- https://bibliotekanauki.pl/articles/1205417.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- We introduce a very weak version of the square principle which may hold even under failure of the generalized continuum hypothesis. Under this weak square principle, we give a new characterization (Theorem 10) of partial orderings with κ-Freese-Nation property (see below for the definition). The characterization is not a ZFC theorem: assuming Chang's Conjecture for $ℵ_ω$, we can find a counter-example to the characterization (Theorem 12). We then show that, in the model obtained by adding Cohen reals, a lot of ccc complete Boolean algebras of cardinality ≤ λ have the $ℵ_1$-Freese-Nation property provided that $μ^{ℵ_0} = μ$ holds for every regular uncountable μ < λ and the very weak square principle holds for each cardinal $ℵ_0 < μ < λ$ of cofinality ω ((Theorem 15). Finally, we prove that there is no $ℵ_2$-Lusin gap if P(ω) has the $ℵ_1$-Freese-Nation property (Theorem 17)
- Źródło:
-
Fundamenta Mathematicae; 1997, 154, 2; 159-176
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł