William Chen-Mertens, Menachem Kojman, Juris Steprāns

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A strong coloring on a cardinal is a function such that for every of full size, every color <![CDATA[ $\unicode{x3b3} is attained by. The symbol asserts the existence of a strong coloring on. We introduce the symbol which asserts the existence of a coloring which is strong over a partition. A coloring f is strong over p if for every there is <![CDATA[ $i so that for every color <![CDATA[ $\unicode{x3b3} is attained by. We prove that whenever holds, also holds for an arbitrary finite partition p. Similarly, arbitrary finite p-s can be added to stronger symbols which hold in any model of ZFC. If, then and stronger symbols, like or, also hold for an arbitrary partition p to parts. The symbols hold for an arbitrary countable partition p under the Continuum Hypothesis and are independent over ZFC CH.

Original languageEnglish
Pages (from-to)67-90
Number of pages24
JournalBulletin of Symbolic Logic
Issue number1
StatePublished - 1 Mar 2021


  • 2020 Mathematics Subject Classification 03E02 03E17 03E35 03E50


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