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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

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

# 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