Martin's axiom and almost disjoint

families

Latifa Faouzi

doi:10.11575/cdm.v2i2.61935

Martin's axiom and almost disjoint families

Authors

Latifa Faouzi

DOI:

https://doi.org/10.11575/cdm.v2i2.61935

Abstract

Assuming

\rfs M A + ℵ_{1} < 2^{ℵ_{0}}

$\rfs{MA} + \aleph_1 < 2^{\aleph_0}$ , we show that, for any

κ, λ < 2^{ℵ_{0}}

$\kappa,\lambda < 2^{\aleph_0}$ and any almost disjoint family

\setn a_{i} i < λ

$\setn{a_i}{i < \lambda}$ of countable subsets of

κ

$\kappa$ , with

λ < 2^{ℵ_{0}}

$\lambda < 2^{\aleph_0}$ , there is a partition

\setn p_{n} n \in ω

$\setn{p_n}{n\in\omega}$ of

κ

$\kappa$ so that

p_{n} \cap a_{i}

$p_n \cap a_i$ is finite for each

(i, n) \in λ \times ω

$(i,n) \in \lambda\times \omega$ .

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Published

2007-11-02

Issue

Vol. 2 No. 2 (2007)

Section

Articles

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