### 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

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

# 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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