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

# 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
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