Temat: PCF - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Embedding Cohen algebras using pcf theory
Autorzy:: Shelah, Saharon
Powiązania:: https://bibliotekanauki.pl/articles/1204996.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: set theory
pcf
forcing
Opis:: Using a theorem from pcf theory, we show that for any singular cardinal ν, the product of the Cohen forcing notions on κ, κ < ν, adds a generic for the Cohen forcing notion on $ν^+$.
Źródło:: Fundamenta Mathematicae; 2000, 166, 1-2; 83-86
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Cellularity of free products of Boolean algebras (or topologies)
Autorzy:: Shelah, Saharon
Powiązania:: https://bibliotekanauki.pl/articles/1205001.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: set theory
pcf
Boolean algebras
cellularity
product
colourings
Opis:: The aim this paper is to present an answer to Problem 1 of Monk [10], [11]. We do this by proving in particular that if μ is a strong limit singular cardinal, $θ = (2^{cf(μ)})^+$ and $2^μ = μ^+$ then there are Boolean algebras $\mathbb{B}_1,\mathbb{B}_2$ such that
$c(\mathbb{B}_1) = μ, c(\mathbb{B}_2) < θ but c(\mathbb{B}_1*\mathbb{B}_2)=μ^+$.
Further we improve this result, deal with the method and the necessity of the assumptions. In particular we prove that if $\mathbb{B}$ is a ccc Boolean algebra and $μ^{ℶ_ω} ≤ λ = cf(λ) ≤ 2^μ$ then $\mathbb{B}$ satisfies the λ-Knaster condition (using the "revised GCH theorem").
Źródło:: Fundamenta Mathematicae; 2000, 166, 1-2; 153-208
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

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

Skocz do pozycji: 4.

Tytuł:: On what I do not understand (and have something to say): Part I
Autorzy:: Shelah, Saharon
Powiązania:: https://bibliotekanauki.pl/articles/1204995.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: set theory
cardinal arithmetic
pcf theory
forcing
iterated forcing
large continuum
nep
nicely definable forcing
combinatorial set theory
Boolean algebras
set-theoretic algebra
partition calculus
Ramsey theory
Opis:: This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdotes and opinions. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history and side references are erratic, usually kept to a minimum ("see ..." means: see the references there and possibly the paper itself). The base were lectures in Rutgers, Fall '97, and reflect my knowledge then. The other half, [122], concentrating on model theory, will subsequently appear. I thank Andreas Blass and Andrzej Rosłanowski for many helpful comments.
Źródło:: Fundamenta Mathematicae; 2000, 166, 1-2; 1-82
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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