### Archives

### 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

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

# 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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