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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

### Keywords

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

# Tag Archives: 05C15

## 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