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- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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