### 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

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

# Blog Archives

## 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

## 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

## More notions of forcing add a Souslin tree

Joint work with Ari Meir Brodsky. Abstract. An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing … 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