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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

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

# Tag Archives: Chromatic number

## 2017 Workshop in Set Theory, Oberwolfach

I gave an invited talk at the Set Theory workshop in Obwerwolfach, February 2017. Talk Title: Coloring vs. Chromatic. Abstract: In a joint work with Chris Lambie-Hanson, we study the interaction between compactness for the chromatic number (of graphs) and … Continue reading

Posted in Invited Talks
Tagged Chromatic number, coloring number, incompactness, stationary reflection
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## 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
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## INFTY Final Conference, March 2014

I gave an invited talk at the INFTY Final Conference meeting, Bonn, March 4-7, 2014. [Curiosity: Georg Cantor was born March 3, 1845] Title: Same Graph, Different Universe. Abstract: In a paper from 1998, answering a question of Hajnal, Soukup … Continue reading

## 2013 Set Theory Programme on Large Cardinals and Forcing

I gave an invited talk at the Large Cardinals and Forcing meeting, Erwin Schrödinger International Institute for Mathematical Physics, Vienna, September 23–27, 2013. Talk Title: Hedetniemi’s conjecture for uncountable graphs Abstract: It is proved that in Godel’s constructible universe, for … Continue reading

Posted in Invited Talks
Tagged Almost countably chromatic, Chromatic number, Hedetniemi's conjecture
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## 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
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## The chromatic numbers of the Erdos-Hajnal graphs

Recall that a coloring $c:G\rightarrow\kappa$ of an (undirected) graph $(G,E)$ is said to be chromatic if $c(v_1)\neq c(v_2)$ whenever $\{v_1,v_2\}\in E$. Then, the chromatic number of a graph $(G,E)$ is the least cardinal $\kappa$ for which there exists a chromatic … Continue reading

Posted in Blog, Expository
Tagged Chromatic number, Erdos-Hajnal graphs, Rado's conjecture, reflection principles
11 Comments