Displaying similar documents to “Counting partial types in simple theories”

On what I do not understand (and have something to say): Part I

Saharon Shelah (2000)

Fundamenta Mathematicae

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This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdotes and opinions. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history...

Embedding Cohen algebras using pcf theory

Saharon Shelah (2000)

Fundamenta Mathematicae

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Using a theorem from pcf theory, we show that for any singular cardinal ν, the product of the Cohen forcing notions on κ, κ < ν, adds a generic for the Cohen forcing notion on ν + .

Definition of Flat Poset and Existence Theorems for Recursive Call

Kazuhisa Ishida, Yasunari Shidama, Adam Grabowski (2014)

Formalized Mathematics

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This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge....

Weak variants of Martin's Axiom

J. Barnett (1992)

Fundamenta Mathematicae

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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...

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. ...

Countably metacompact spaces in the constructible universe

Paul Szeptycki (1993)

Fundamenta Mathematicae

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We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a G δ . In addition some nonperfect spaces with σ-disjoint bases are constructed.

A generalization of a generic theorem in the theory of cardinal invariants of topological spaces

Alejandro Ramírez-Páramo, Noé Trinidad Tapia-Bonilla (2007)

Commentationes Mathematicae Universitatis Carolinae

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The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel’skii’s inequality: If X is a T 2 -space, then | X | ≤ 2 L ( X ) χ ( X ) . Moreover, we will show relative versions of three well-known cardinal inequalities.