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Displaying similar documents to “Axioms which imply GCH”

Lusin sequences under CH and under Martin's Axiom

Uri Abraham, Saharon Shelah (2001)

Fundamenta Mathematicae

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Assuming the continuum hypothesis there is an inseparable sequence of length ω₁ that contains no Lusin subsequence, while if Martin's Axiom and ¬ CH are assumed then every inseparable sequence (of length ω₁) is a union of countably many Lusin subsequences.

New axioms in set theory

Giorgio Venturi, Matteo Viale (2018)

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana

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In this article we review the present situation in the foundations of set theory, discussing two programs meant to overcome the undecidability results, such as the independence of the continuum hypothesis; these programs are centered, respectively, on forcing axioms and Woodin's V = Ultimate-L conjecture. While doing so, we briefly introduce the key notions of set theory.

Non-separating subcontinua of planar continua

D. Daniel, C. Islas, R. Leonel, E. D. Tymchatyn (2015)

Colloquium Mathematicae

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We revisit an old question of Knaster by demonstrating that each non-degenerate plane hereditarily unicoherent continuum X contains a proper, non-degenerate subcontinuum which does not separate X.

Induced open projections and C*-smoothness

Włodzimierz J. Charatonik, Alejandro Illanes, Verónica Martínez-de-la-Vega (2013)

Colloquium Mathematicae

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We show that there exists a C*-smooth continuum X such that for every continuum Y the induced map C(f) is not open, where f: X × Y → X is the projection. This answers a question of Charatonik (2000).

1/2-Homogeneous hyperspace suspensions

Sergio Macías, Patricia Pellicer-Covarrubias (2012)

Colloquium Mathematicae

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We continue the study of 1/2-homogeneity of the hyperspace suspension of continua. We prove that if X is a decomposable continuum and its hyperspace suspension is 1/2-homogeneous, then X must be continuum chainable. We also characterize 1/2-homogeneity of the hyperspace suspension for several classes of continua, including: continua containing a free arc, atriodic and decomposable continua, and decomposable irreducible continua about a finite set.