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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

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

# Tag Archives: incompactness

## 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

## 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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