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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

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

# 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