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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

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

# Tag Archives: Postprocessing function

## Distributive Aronszajn trees

Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading

## 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