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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

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

# 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