TY - JOUR

T1 - STRONG COLORINGS over PARTITIONS

AU - Chen-Mertens, William

AU - Kojman, Menachem

AU - Steprāns, Juris

N1 - Funding Information:
The first author’s research for this paper was partially supported by an Israeli Science Foundation grant number 665/20. The third author’s research for this paper was partially supported by NSERC of Canada.
Publisher Copyright:
© 2021 Cambridge University Press. All rights reserved.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - 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.

AB - 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.

KW - 2020 Mathematics Subject Classification 03E02 03E17 03E35 03E50

UR - http://www.scopus.com/inward/record.url?scp=85106089028&partnerID=8YFLogxK

U2 - 10.1017/bsl.2021.5

DO - 10.1017/bsl.2021.5

M3 - Article

AN - SCOPUS:85106089028

VL - 27

SP - 67

EP - 90

JO - Bulletin of Symbolic Logic

JF - Bulletin of Symbolic Logic

SN - 1079-8986

IS - 1

ER -