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<p>The paper deals with two notions: polarized partition relations and the product of generalized strong sequences. Strong sequences were introduced by Efimov in 1965 as a useful tool for proving famous theorems in dyadic spaces, i.e. continuous image of the Cantor cube. In this paper we introduce the notion of the product of generalized strong sequences and give a pure combinatorial proof that the existence of the product of generalized strong sequences is equivalent to polarized partition relations.</p>

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On equivalences of polarized partition relations

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Joanna Jureczko

摘要

The paper deals with two notions: polarized partition relations and the product of generalized strong sequences. Strong sequences were introduced by Efimov in 1965 as a useful tool for proving famous theorems in dyadic spaces, i.e. continuous image of the Cantor cube. In this paper we introduce the notion of the product of generalized strong sequences and give a pure combinatorial proof that the existence of the product of generalized strong sequences is equivalent to polarized partition relations.