The Covering Property Axiom, CPA

Ciesielski, Krzysztof; Pawlikowski, Janusz

doi:10.1017/cbo9780511546457

Cited by 37 publications

(38 citation statements)

References 90 publications

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“…Also recall that it is consistent that cof(N ω ) = ω 1 < c; this is so in the Sacks model, see e.g. [5]. Theorem 3.3 Assuming cof(N ω ) = ω 1 there is a Boolean algebra B of cardinality ω 1 such that B has a strictly positive measure but carries no strictly positive separable measure.…”

Section: 1mentioning

confidence: 91%

Strictly positive measures on Boolean algebras

Džamonja

Plebanek

2008

J. symb. log.

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Section: 1mentioning

confidence: 91%

Strictly positive measures on Boolean algebras

Džamonja

Plebanek

2008

J. symb. log.

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“…Under the CPA, Covering Property Axiom (see [32] for details), we have that SZ \.D [ S/ D ¿ (hence SZ \ ES D ¿).…”

Section: Sierpiński-zygmund Functionsmentioning

confidence: 99%

A hierarchy in the family of real surjective functions

et al. 2017

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This expository paper focuses on the study of extreme surjective functions in R R . We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, Ä-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The algebraic structure of the sets of surjective functions we show here is studied using the concept of lineability. In the final sections of this work we also reveal unexpected connections between the different degrees of extreme surjectivity given above and other interesting sets of functions such as the space of additive mappings, the class of mappings with a dense graph, the class of Darboux functions and the class of Sierpiński-Zygmund functions in R R .

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“…The cardinality of R is denoted by c. By ZFC we mean Zermelo-Fraenkel set theory with the axiom of choice, by CPA we mean the Covering Property Axiom, see e.g. [7], and by CH we mean the Continuum Hypothesis. In this paper we always consider R as a linear space over Q, except in subsection 3.3 where it is explicitly indicated otherwise.…”

Section: Preliminariesmentioning

confidence: 99%

On some properties of Hamel bases and their applications to Marczewski measurable functions

2013

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Abstract:We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist.Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions. MSC:

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The Covering Property Axiom, CPA

Cited by 37 publications

References 90 publications

Strictly positive measures on Boolean algebras

Strictly positive measures on Boolean algebras

A hierarchy in the family of real surjective functions

On some properties of Hamel bases and their applications to Marczewski measurable functions

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