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### Recent blog posts

- 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

### Keywords

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

# 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