Same graph, different universe

Assaf Rinot

doi:10.1007/s00153-017-0551-x

Same graph, different universe

Assaf Rinot

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 G_μ satisfying the following:G_μ has size and chromatic number μ;for every infinite cardinal κ< μ, there exists a cofinality-preserving GCH -preserving forcing extension in which Chr (G_μ) = κ.

Original language	English
Pages (from-to)	783-796
Number of pages	14
Journal	Archive for Mathematical Logic
Volume	56
Issue number	7-8
DOIs	https://doi.org/10.1007/s00153-017-0551-x
State	Published - 1 Nov 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

Funding

Partially supported by ISF Grant 1630/14.

Funders	Funder number
Israel Science Foundation	1630/14

Keywords

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

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10.1007/s00153-017-0551-x

Cite this

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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 G{\"o}del{\textquoteright}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.",

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Same graph, different universe

Abstract

Bibliographical note

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Keywords

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