### 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

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

# 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