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arXiv · 1805.06028

An uncountable version of Pt\'ak's combinatorial lemma

Petr Hájek·Tommaso Russo
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Abstract

In this note we are concerned with the validity of an uncountable analogue of a combinatorial lemma due to Vlastimil Pt\'ak. We show that the validity of the result for $\omega_1$ can not be decided in ZFC alone. We also provide a sufficient condition, for a class of larger cardinals.

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Petr Hájek, Tommaso Russo. 2018-05-15. An uncountable version of Pt\'ak's combinatorial lemma. https://doi.org/10.1016/j.jmaa.2018.10.049

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