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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

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

# 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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