Specializing Aronszajn tree and preserving some weak diamonds

• Autorzy: Mildenberger H. , Shelah S.
• Języki publikacji: EN

Abstrakty

EN

We show that [wzór) together with CH and "all Aronszajn trees are special" is consistent relative to ZFC. The weak diamond for the covering relation of Lebesgue null sets was the only weak diamond in the Cichori diagramrne for relations whose consistency together with "all Aronszajn trees are special" was not yet settled. Our forcing proof gives also new proofs to the known consistencies of several other weak diamonds stemming from the Cichori diagramme together with "all Aronszajn trees are special" and CH. The main part of our work is an application [15, Chapter V, §§ 1-7] for a special completeness system, such that we have a genericity game. Thus we show new preservation properties of the known forcings.

Słowa kluczowe

EN

independence from ZFC; forcing; special Aronszajn tree; weak diamond

PL

niezależność z ZFC; tłoczenie; specjalne drzewo Aronszajna; słabe diamenty

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2009
• Tom: Vol. 15, nr 1
• Strony: 47--78
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Mildenberger H.

autor

Shelah S.

• Uniwersität Wien Kurt Gödel Research Center for Mathematical Logic,

Bibliografia

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