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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

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

# Tag Archives: Chromatic number

## MFO workshop in Set Theory, February 2017

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

## Set Theory Programme on Large Cardinals and Forcing, September 2013

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