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### Recent blog posts

- 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
- Partitioning the club guessing January 22, 2014

### Keywords

Prikry-type forcing Ascent Path incompactness Uniformization diamond star Mandelbrot set Rock n' Roll Cardinal Invariants Commutative cancellative semigroups HOD Hereditarily Lindelöf space Kurepa Hypothesis 05A17 Microscopic Approach Nonspecial tree Cardinal function Almost Souslin Martin's Axiom Absoluteness tensor product graph Square-Brackets Partition Relations Parameterized proxy principle Fast club Rado's conjecture Dushnik-Miller Club Guessing reflection principles S-Space Constructible Universe Large Cardinals Foundations Successor of Singular Cardinal Successor of Regular Cardinal middle diamond Coherent tree Uniformly coherent polarized partition relation b-scale very good scale Axiom R Erdos-Hajnal graphs Stevo Todorcevic Prevalent singular cardinals 05D10 Reduced Power Distributive tree 20M14 Jonsson cardinal Cohen real Hindman's Theorem Chang's conjecture Shelah's Strong Hypothesis Antichain Almost countably chromatic Poset Almost-disjoint famiy Slim tree stationary hitting Sakurai's Bell inequality Chromatic number Singular coﬁnality Forcing Axioms P-Ideal Dichotomy Postprocessing function Non-saturation stationary reflection free Boolean algebra projective Boolean algebra Partition Relations OCA 11P99 weak square coloring number Ostaszewski square Singular cardinals combinatorics square principles Aronszajn tree Hedetniemi's conjecture Singular Density Minimal Walks sap Diamond PFA(S)[S] Selective Ultrafilter Fodor-type reflection approachability ideal Forcing ccc xbox Fat stationary set L-space Whitehead Problem Erdos Cardinal Weakly compact cardinal square Knaster Rainbow sets Small forcing PFA weak diamond Generalized Clubs Universal Sequences Souslin Tree

# Tag Archives: Microscopic Approach

## 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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