Banach spaces and large cardinals

Jussi Ketonen

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Displaying similar documents to “Banach spaces and large cardinals”

Properties of the gimel function and a classification of singular cardinals

Thomas Jech (1973)

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A generalized version of the singular cardinals problem

Arthur Apter (1984)

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A result on the isomorphic embeddability of l¹(Γ)

S. Argyros, J. Bourgain, T. Zachariades (1984)

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Singular cardinals and strong extenders

Arthur Apter, James Cummings, Joel Hamkins (2013)

Open Mathematics

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We investigate the circumstances under which there exist a singular cardinal µ and a short (κ,µ)-extender E witnessing “κ is µ-strong”, such that µ is singular in Ult(V, E).

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F. Drake (1970)

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Collectionwise Hausdorffness at limit cardinals

Nobuyuki Kemoto (1991)

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Hybrid Prikry forcing

Dima Sinapova (2015)

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We present a new forcing notion combining diagonal supercompact Prikry forcing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ, and GCH holds below κ. Moreover we define a scale at κ which has a stationary set of bad points in the ground model.

Two set-theoretic problems in topology

Juhász, I.

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Hereditarily finitely decomposable Banach spaces

V. Perenczi (1997)

Studia Mathematica

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A Banach space is said to be $H D_{n}$ if the maximal number of subspaces of X forming a direct sum is finite and equal to n. We study some properties of $H D_{n}$ spaces, and their links with hereditarily indecomposable spaces; in particular, we show that if X is complex $H D_{n}$ , then dim $(ℒ (X) / S (X)) \leq n^{2}$ , where S(X) denotes the space of strictly singular operators on X. It follows that if X is a real hereditarily indecomposable space, then ℒ(X)/S(X) is a division ring isomorphic either to ℝ, ℂ, or ℍ, the quaternionic...