Coloring finite subsets of uncountable sets

Authors:
Péter Komjáth and Saharon Shelah

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3501-3505

MSC (1991):
Primary 03E35

MathSciNet review:
1342032

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Abstract: It is consistent for every that and there is a function such that every finite set can be written in at most ways as the union of two distinct monocolored sets. If GCH holds, for every such coloring there is a finite set that can be written at least ways as the union of two sets with the same color.

**1.**James E. Baumgartner and Saharon Shelah,*Remarks on superatomic Boolean algebras*, Ann. Pure Appl. Logic**33**(1987), no. 2, 109–129. MR**874021**, 10.1016/0168-0072(87)90077-7**2.**S. Ghosh,*On the theory of sets*, Bull. Calcutta Math. Soc.**78**(1986), no. 2, 81–83. MR**852076****3.**P. Erdös and R. Rado,*A partition calculus in set theory*, Bull. Amer. Math. Soc.**62**(1956), 427–489. MR**0081864**, 10.1090/S0002-9904-1956-10036-0**4.**M. Gilchrist and S. Shelah,*On identities of colorings of pairs for*(to appear).**5.**P. Komjáth,*A set mapping with no infinite free subsets*, J. Symbolic Logic**56**(1991), no. 4, 1400–1402. MR**1136466**, 10.2307/2275484**6.**P. Komjáth and S. Shelah,*On uniformly antisymmetric functions*, Real Anal. Exchange**19**(1993/94), no. 1, 218–225. MR**1268847****7.**Saharon Shelah and Lee Stanley,*A theorem and some consistency results in partition calculus*, Ann. Pure Appl. Logic**36**(1987), no. 2, 119–152. MR**911579**, 10.1016/0168-0072(87)90015-7

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Additional Information

**Péter Komjáth**

Affiliation:
Department of Computer Science, Eötvös University, Budapest, Múzeum krt. 6–8, 1088, Hungary

Email:
kope@cs.elte.hu

**Saharon Shelah**

Affiliation:
Institute of Mathematics, Hebrew University, Givat Ram, 91904, Jerusalem, Israel

Email:
shelah@math.huji.ac.il

DOI:
https://doi.org/10.1090/S0002-9939-96-03450-8

Keywords:
Axiomatic set theory,
independence proofs,
combinatorial set theory

Received by editor(s):
March 31, 1995

Received by editor(s) in revised form:
May 9, 1995

Additional Notes:
The first author was supported by the Hungarian OTKA, Grant No. T014105.\endgraf This paper is number 516 in the cumulative list of Shelah’s papers. His research was supported by the Basic Research Foundation of the Israel Academy of Sciences and Humanities.

Communicated by:
Andreas R. Blass

Article copyright:
© Copyright 1996
American Mathematical Society