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 language | English |
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Pages (from-to) | 783-796 |
Number of pages | 14 |
Journal | Archive for Mathematical Logic |
Volume | 56 |
Issue number | 7-8 |
DOIs | |
State | Published - 1 Nov 2017 |
Keywords
- C-sequence graph
- Cardinal fixed-point
- Chromatic spectrum
- Mutual stationarity
All Science Journal Classification (ASJC) codes
- Philosophy
- Logic