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Periodica Mathematica Hungarica

, Volume 21, Issue 1, pp 1–7 | Cite as

On c+-chromatic graphs with small bounded subgraphs

  • L. Soukup
Article

Abstract

It is shown that if ZF is consistent then so is ZFC+2ω is as large as you wish + “there is a graph with cardinality and chromatic number (2ω) + such that every subgraph of cardinality ≤2ω has chromatic number ω”.

Mathematics subject classification numbers, 1980/85

Primary 03E35 Secondary 04A20 

Key words and phrases

Chromatic number forcing Martin's axiom 

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References

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    J. E.Baumgartner, Generich graph construction,J. Symbolic Logic 49 (1984), 234–240.Zbl 573: 03021Google Scholar
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    P.Erdős, Problems and results on finite and infinite combinatorial analysis,Infinite and finite sets, I (Collog. Math. Soc. J. Bolyai, 10,Keszthely, 1973), North-Holland, Amsterdam, 1975; 403–323.MR 52: 10438Google Scholar
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    P.Erdős, A.Hajnal, A.Máté and R.Rado,Combinatorial set theory: Partition relations for cardinals, Akadémiai Kiadó, Budapest, 1984.Zbl 573: 03019Google Scholar
  4. [4]
    T.Jech,Set theory, Academic Press, New York, 1978.MR 80a: 03062Google Scholar

Copyright information

© Akadémiai Kiadó 1990

Authors and Affiliations

  • L. Soukup
    • 1
  1. 1.MTA Matematikai KutatóintézetBudapestHungary

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