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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

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

# 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