Same graph, different universe

Assaf Rinot

doi:10.1007/s00153-017-0551-x

Same graph, different universe

Assaf Rinot

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
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Philosophy
Logic

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10.1007/s00153-017-0551-x

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title = "Same graph, different universe",

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.",

keywords = "C-sequence graph, Cardinal fixed-point, Chromatic spectrum, Mutual stationarity",

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AB - 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.

KW - C-sequence graph

KW - Cardinal fixed-point

KW - Chromatic spectrum

KW - Mutual stationarity

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ER -

Same graph, different universe

Abstract

Keywords

ASJC Scopus subject areas

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