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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

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

# Category Archives: Infinite Graphs

## 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