### 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

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

# Tag Archives: 05C05

## 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

## A Microscopic approach to Souslin-tree constructions. Part I

Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading

Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
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## 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