### 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

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

# Tag Archives: free Souslin tree

## 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

## Reduced powers of Souslin trees

Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading