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### Recent blog posts

- 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

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

# Tag Archives: Chang’s conjecture

## 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

## Strong failures of higher analogs of Hindman’s Theorem

Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading