### Archives

### 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

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

# 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