### Archives

### 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

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

# Tag Archives: Postprocessing function

## A remark on Schimmerling’s question

Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading

## The 14th International Workshop on Set Theory in Luminy

I gave an invited talk at the 14th International Workshop on Set Theory in Luminy in Marseille, October 2017. Talk Title: Distributive Aronszajn trees Abstract: It is well-known that that the statement “all $\aleph_1$-Aronszajn trees are special” is consistent with ZFC … Continue reading

## 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