### 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

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

# 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