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Displaying similar documents to “Preserving some properties of large cardinals under mild Cohen extensions”

Extensions with the approximation and cover properties have no new large cardinals

Joel David Hamkins (2003)

Fundamenta Mathematicae

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If an extension V ⊆ V̅ satisfies the δ approximation and cover properties for classes and V is a class in V̅, then every suitably closed embedding j: V̅ → N̅ in V̅ with critical point above δ restricts to an embedding j ↾ V amenable to the ground model V. In such extensions, therefore, there are no new large cardinals above δ. This result extends work in [Ham01].

Compactification-like extensions

M. R. Koushesh

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Let X be a space. A space Y is called an extension of X if Y contains X as a dense subspace. For an extension Y of X the subspace Y∖X of Y is called the remainder of Y. Two extensions of X are said to be equivalent if there is a homeomorphism between them which fixes X pointwise. For two (equivalence classes of) extensions Y and Y' of X let Y ≤ Y' if there is a continuous mapping of Y' into Y which fixes X pointwise. Let 𝓟 be a topological property. An extension Y of X is called a 𝓟-extension...

Adding a lot of Cohen reals by adding a few. II

Moti Gitik, Mohammad Golshani (2015)

Fundamenta Mathematicae

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We study pairs (V, V₁), V ⊆ V₁, of models of ZFC such that adding κ-many Cohen reals over V₁ adds λ-many Cohen reals over V for some λ > κ.

Definable quantifiers in second order arithmetic and elementary extensions of ω-models

Wojciech Guzicki

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CONTENTS0. Introduction and terminology..............................................................51. Quantifiers and elementary extensions..............................................82. Elementary extensions of countable models of set theory................153. Interpretations of set theory in extensions of A₂...............................214. Definable quantifiers in models of A₂...............................................325. Elementary generic extensions........................................................40References..........................................................................................50 ...