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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

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

# Tag Archives: Microscopic Approach

## A remark on Schimmerling’s question

Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading

## 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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