Free sets for a set-mapping relative to a family of sets

Antonio Avilés; Claribet Piña

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arXiv · 1607.03291

Free sets for a set-mapping relative to a family of sets

Antonio Avilés·Claribet Piña

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Abstract

Given a family $\mathcal{F}$ of subsets of $\{1,\ldots,m\}$, we try to compute the least natural number $n$ such that for every function $S:[\aleph_n]^{<\omega}\longrightarrow [\aleph_n]^{<\omega}$ there exists a bijection $u:\{1,\ldots,m\}\longrightarrow Y\subset \aleph_n$ such that $Su(A)\cap Y \subset u(A)$ for all $A\in\mathcal{F}$.

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BibTeX RIS

Antonio Avilés, Claribet Piña. 2016-07-12. Free sets for a set-mapping relative to a family of sets. https://arxiv.org/abs/1607.03291

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