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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

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Cardinal function Antichain Absoluteness Cardinal Invariants Luzin set Distributive tree PFA Erdos-Hajnal graphs Fat stationary set Rainbow sets reflection principles Square-Brackets Partition Relations Singular coﬁnality Parameterized proxy principle Nonspecial tree Hedetniemi's conjecture 05A17 b-scale projective Boolean algebra HOD Stevo Todorcevic Rado's conjecture Mandelbrot set Slim tree xbox tensor product graph 05D10 weak diamond Cohen real 11P99 weak square middle diamond sap Prevalent singular cardinals 20M14 Chang's conjecture coloring number Axiom R incompactness Microscopic Approach Minimal Walks Club Guessing Martin's Axiom Hereditarily Lindelöf space Constructible Universe Commutative cancellative semigroups Rock n' Roll Reduced Power polarized partition relation Singular cardinals combinatorics S-Space Souslin Tree Almost Souslin Weakly compact cardinal Knaster Whitehead Problem PFA(S)[S] Sakurai's Bell inequality Ascent Path Dushnik-Miller Jonsson cardinal very good scale Chromatic number Kurepa Hypothesis Diamond P-Ideal Dichotomy L-space Selective Ultrafilter Fast club Large Cardinals Prikry-type forcing stationary hitting Forcing Axioms approachability ideal Forcing Successor of Singular Cardinal Uniformly coherent Coherent tree Small forcing OCA Almost-disjoint famiy diamond star square Hindman's Theorem Postprocessing function Singular Density Fodor-type reflection Aronszajn tree Non-saturation Poset ccc Partition Relations Shelah's Strong Hypothesis Foundations Uniformization Erdos Cardinal Successor of Regular Cardinal Ostaszewski square free Boolean algebra Almost countably chromatic square principles stationary reflection Universal Sequences Generalized Clubs

# Tag Archives: 05C63

## Reflection on the coloring and chromatic numbers

Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading

## 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 Godel’s constructible … Continue reading

Posted in Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
10 Comments

## Hedetniemi’s conjecture for uncountable graphs

Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal $\kappa$, there exist graphs $\mathcal G$ and $\mathcal H$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal G\times\mathcal H$ is countably chromatic. … Continue reading

## Chromatic numbers of graphs – large gaps

Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading

Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments