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Displaying 101 – 120 of 436

Decomposing Baire class 1 functions into continuous functions

Saharon Shelah, Juris Steprans (1994)

Fundamenta Mathematicae

It is shown to be consistent that every function of first Baire class can be decomposed into $ℵ_{1}$ continuous functions yet the least cardinal of a dominating family in $^{ω} ω$ is $ℵ_{2}$ . The model used in the one obtained by adding $ω_{2}$ Miller reals to a model of the Continuum Hypothesis.

Dedekind-Endlichkeit und Wohlordenbarkeit.

Norbert Brunner (1982)

Monatshefte für Mathematik

Definitions of finite

Paul Howard, Mary Yorke (1989)

Fundamenta Mathematicae

Definitions of finiteness based on order properties

Omar De la Cruz, Damir D. Dzhafarov, Eric J. Hall (2006)

Fundamenta Mathematicae

A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Choice (AC) is assumed, is equivalent to stating that the set is finite; several such definitions have been studied over the years. In this article we introduce a framework for generating definitions of finiteness in a systematical way: basic definitions are obtained from properties of certain classes of binary relations, and further definitions are obtained from the basic ones by closing them under subsets...

Degrees of dependence in the theory of semisets.

Petr Hájek (1974)

Fundamenta Mathematicae

Dense orderings, partitions and weak forms of choice

Carlos González (1995)

Fundamenta Mathematicae

We investigate the relative consistency and independence of statements which imply the existence of various kinds of dense orders, including dense linear orders. We study as well the relationship between these statements and others involving partition properties. Since we work in ZF (i.e. without the Axiom of Choice), we also analyze the role that some weaker forms of AC play in this context

Destroying precaliber $ℵ_{1}$ : an application of a Δ-systems lemma for closed sets

Juris Steprans, Stephen Watson (1988)

Fundamenta Mathematicae

Diamond and λ-systems

Alan Makler, Saharon Shelah (1988)

Fundamenta Mathematicae

Disjoint refinement and related topics

Balcar, B., Simon, P., Vojtáš, P. (1980)

Abstracta. 8th Winter School on Abstract Analysis

Distinguishing Lindelöfness and inverse Lindelöfness

Viacheslav I. Malykhin (1995)

Commentationes Mathematicae Universitatis Carolinae

On $ω_{1}$ a Hausdorff inverse Lindelöf non Lindelöf topology has been constructed.

Distinguishing two partition properties of ω1

Péter Komjáth (1998)

Fundamenta Mathematicae

It is consistent that $ω_{1} \to {(ω_{1}, (ω : 2))}^{2}$ but $ω_{1} ↛ {(ω_{1}, ω + 2)}^{2}$ .

Dualization of van Douwen diagram

Jacek Cichoń, Barbara Majcher-Iwanow, Bogdan Węglorz (1992)

Acta Universitatis Carolinae. Mathematica et Physica

Easton functions and supercompactness

Brent Cody, Sy-David Friedman, Radek Honzik (2014)

Fundamenta Mathematicae

Suppose that κ is λ-supercompact witnessed by an elementary embedding j: V → M with critical point κ, and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton’s theorem: (1) ∀α α < cf(F(α)), and (2) α < β ⇒ F(α) ≤ F(β). We address the question: assuming GCH, what additional assumptions are necessary on j and F if one wants to be able to force the continuum function to agree with F globally, while preserving...

Edge decompositions of graphs with no large independent sets.

Galvin, F., Hajnal, A., Komjáth, P. (1995)

Publications de l'Institut Mathématique. Nouvelle Série

Embedding of Boolean algebras in Ρ(ω)/fin

J. Baumgartner, R. Frankiewicz, P. Zbierski (1990)

Fundamenta Mathematicae

Embedding orders into the cardinals with $D C_{κ}$

Asaf Karagila (2014)

Fundamenta Mathematicae

Jech proved that every partially ordered set can be embedded into the cardinals of some model of ZF. We extend this result to show that every partially ordered set can be embedded into the cardinals of some model of $Z F + D C_{< κ}$ for any regular κ. We use this theorem to show that for all κ, the assumption of $D C_{κ}$ does not entail that there are no decreasing chains of cardinals. We also show how to extend the result to and embed into the cardinals a proper class which is definable over the ground model. We use...

Embedding partially ordered sets into $^{ω} ω$

Ilijas Farah (1996)

Fundamenta Mathematicae

We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion $H_{E}$ which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).

Embeddings into 𝓟(ℕ)/fin and extension of automorphisms

A. Bella, A. Dow, K. P. Hart, M. Hrusak, J. van Mill, P. Ursino (2002)

Fundamenta Mathematicae

Given a Boolean algebra 𝔹 and an embedding e:𝔹 → 𝓟(ℕ)/fin we consider the possibility of extending each or some automorphism of 𝔹 to the whole 𝓟(ℕ)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.

Errata to the paper "Models of second order arithmetic with definable Skolem functions", Fundamenta Mathematicae 75 (1972), pp. 223-234

Andrzej Mostowski (1974)

Fundamenta Mathematicae

Evasion and prediction - the Specker phenomenon and Gross space.

Jörg Brendle (1995)

Forum mathematicum

Currently displaying 101 – 120 of 436

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