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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
- Genearlizations 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

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

# 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 Preprints, 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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