# On incompactness for chromatic number of graphs

@article{Shelah2012OnIF, title={On incompactness for chromatic number of graphs}, author={Saharon Shelah}, journal={Acta Mathematica Hungarica}, year={2012}, volume={139}, pages={363-371} }

We deal with incompactness. Assume the existence of non-reflecting stationary set of cofinality κ. We prove that one can define a graph G whose chromatic number is >κ, while the chromatic number of every subgraph G′⫅G, |G′|<|G| is ≦κ. The main case is κ=ℵ0.

## 7 Citations

Chromatic numbers of graphs — large gaps

- Mathematics, Computer ScienceComb.
- 2015

It is proved that if 0# does not exist, then for every singular strong limit cardinal λ, there exists an (ℵ0,λ+)-chromatic graph of size λ+.

Reflection on the Coloring and Chromatic Numbers

- Mathematics, Computer ScienceComb.
- 2019

It is proved that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number and that, in contrast to thechromatic number, the coloringNumber does not admit arbitrarily large incompactness gaps.

Combinatorial Principles and some questions concerning L-like properties and DC$_{\kappa}$

- Mathematics
- 2019

We extend a result of Arthur Apter which answer a question of Matthew Foreman and Menachem Magidor related to mutually stationary sets. We also extend a result of Arthur Apter which answer a question…

Quite free complicated abelian groups, pcf and black boxes

- Mathematics
- 2014

We like to build Abelian groups (or R-modules) which on the one hand are quite free, say $\aleph_{\omega + 1}$-free, and on the other hand, are complicated in suitable sense. We choose as our test…

STATIONARY REFLECTION

- Computer Science, MathematicsThe Journal of Symbolic Logic
- 2020

The upper bound for the consistency strength of stationary reflection at successors of singular cardinals is improved, which is in line with previous work on this topic.

ERDŐS AND SET THEORY

- Computer ScienceThe Bulletin of Symbolic Logic
- 2014

Paul Erdős (26 March 1913—20 September 1996) was a mathematician par excellence whose results and initiatives have had a large impact and made a strong imprint on the doing of and thinking about…

LIST OF PUBLICATIONS

- 2022

1. Sh:a Saharon Shelah. Classification theory and the number of nonisomorphic models, volume 92 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam-New…

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