Temat: forcing set - 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:: 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

Skocz do pozycji: 3.

Tytuł:: On a problem of Steve Kalikow
Autorzy:: Shelah, Saharon
Powiązania:: https://bibliotekanauki.pl/articles/1205000.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: set theory
forcing
continuity
Kalikow
free subset
Opis:: The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for $ℵ_ω$ but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants.
Źródło:: Fundamenta Mathematicae; 2000, 166, 1-2; 137-151
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Almost disjoint families and property (a)
Autorzy:: Szeptycki, Paul
Vaughan, Jerry
Powiązania:: https://bibliotekanauki.pl/articles/1205285.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: property (a), density
extent
almost disjoint families
Ψ-space
CH
GCH
Martin's Axiom
$\got p = \got c$
Cohen forcing
Q-set
weakly inaccessible cardinal.
Opis:: We consider the question: when does a Ψ-space satisfy property (a)? We show that if $|A| < \got p$ then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality $\got p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).
Źródło:: Fundamenta Mathematicae; 1998, 158, 3; 229-240
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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