On Extensions of Elementary Submodels by Forcing

On Extensions of Elementary Submodels by Forcing

We study when a partial order ℙ preserves certain properties of an elementary submodel (of a structure of the form Hθ), including countable closure and ω-covering. In particular, we discuss the existence of ω-covering elementary submodels of different sizes.

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Veröffentlicht in:Logic journal of the IGPL 2007, Vol.15 (5-6), p.637-651
Hauptverfasser: Junqueira, Lúcia R., Larson, Paul, Passos, Marcelo D.
Format: Artikel
Sprache:eng
Schlagworte:
elementary submodels
forcing
ω-covering
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Beschreibung
Zusammenfassung:We study when a partial order ℙ preserves certain properties of an elementary submodel (of a structure of the form Hθ), including countable closure and ω-covering. In particular, we discuss the existence of ω-covering elementary submodels of different sizes.
ISSN:1367-0751
1368-9894
DOI:10.1093/jigpal/jzm043