Weak variants of Martin's Axiom

J. Barnett

Displaying similar documents to “Weak variants of Martin's Axiom”

On a problem of Steve Kalikow

Saharon Shelah (2000)

Fundamenta Mathematicae

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The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for $ℵ_{ω}$ but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants. ...

On the theory of grossone.

Gutman, A.E., Kutateladze, S.S. (2008)

Sibirskij Matematicheskij Zhurnal

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Covering of the null ideal may have countable cofinality

Saharon Shelah (2000)

Fundamenta Mathematicae

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We prove that it is consistent that the covering number of the ideal of measure zero sets has countable cofinality.

A new large cardinal and Laver sequences for extendibles

Paul Corazza (1997)

Fundamenta Mathematicae

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We define a new large cardinal axiom that fits between $A_{3}$ and $A_{4}$ in the hierarchy of axioms described in [SRK]. We use this new axiom to obtain a Laver sequence for extendible cardinals, improving the known large cardinal upper bound for the existence of such sequences.

Homogeneous models and stable diagrams.

Kudajbergenov, K.Zh. (2002)

Sibirskij Matematicheskij Zhurnal

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Goldstern–Judah–Shelah preservation theorem for countable support iterations

Miroslav Repický (1994)

Fundamenta Mathematicae

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[1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362....

On the independence property.

Kudajbergenov, K.Zh. (2000)

Siberian Mathematical Journal

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Extending real-valued functions in βκ

Alan Dow (1997)

Fundamenta Mathematicae

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An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality $c$ and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.

Dominating analytic families

Anastasis Kamburelis (1998)

Fundamenta Mathematicae

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Let A be an analytic family of sequences of sets of integers. We show that either A is dominated or it contains a continuum of almost disjoint sequences. From this we obtain a theorem by Shelah that a Suslin c.c.c. forcing adds a Cohen real if it adds an unbounded real.

Inference rules with metavariables and logical equations in the pretabular modal logic PM1.

Kiyatkin, V.R. (2000)

Siberian Mathematical Journal

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On compact spaces carrying Radon measures of uncountable Maharam type

David Fremlin (1997)

Fundamenta Mathematicae

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If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable $L^{1}$ space, then there is a continuous surjection from X onto ${[0, 1]}^{ω_{1}}$ .

Monotone σ-complete groups with unbounded refinement

Friedrich Wehrung (1996)

Fundamenta Mathematicae

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The real line ℝ may be characterized as the unique non-atomic directed partially ordered abelian group which is monotone σ-complete (countable increasing bounded sequences have suprema), has the countable refinement property (countable sums $\sum_{m} a_{m} = \sum_{n} b_{n}$ of positive (possibly infinite) elements have common refinements) and is linearly ordered. We prove here that the latter condition is not redundant, thus solving an old problem by A. Tarski, by proving that there are many spaces (in particular,...

Forcing tightness in products of fans

Jörg Brendle, Tim La Berge (1996)

Fundamenta Mathematicae

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We prove two theorems that characterize tightness in certain products of fans in terms of families of integer-valued functions. We also define several notions of forcing that allow us to manipulate the structure of the set of functions from some cardinal θ to ω, and hence, the tightness of these products. These results give new constructions of first countable <θ-cwH spaces that are not ≤θ-cwH.