### 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

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

# Tag Archives: Microscopic Approach

## 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

## Forcing and its Applications Retrospective Workshop, April 2015

I gave an invited talk at Forcing and its Applications Retrospective Workshop, Toronto, April 1st, 2015. Title: A microscopic approach to Souslin trees constructions Abstract: We present an approach to construct $\kappa$-Souslin trees that is insensitive to the identity of … Continue reading

Posted in Invited Talks
Tagged Microscopic Approach, Parameterized proxy principle, Souslin Tree
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