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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

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

# 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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