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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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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