Same graph, different universe

Research output: Contribution to journalArticlepeer-review

Abstract

May the same graph admit two different chromatic numbers in two different universes? How about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Gödel’s constructible universe, for every uncountable cardinal μ below the first fixed-point of the ℵ-function, there exists a graph Gμ satisfying the following:Gμ has size and chromatic number μ;for every infinite cardinal κ< μ, there exists a cofinality-preserving GCH -preserving forcing extension in which Chr (Gμ) = κ.

Original languageEnglish
Pages (from-to)783-796
Number of pages14
JournalArchive for Mathematical Logic
Volume56
Issue number7-8
DOIs
StatePublished - 1 Nov 2017

Keywords

  • C-sequence graph
  • Cardinal fixed-point
  • Chromatic spectrum
  • Mutual stationarity

All Science Journal Classification (ASJC) codes

  • Philosophy
  • Logic

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