### 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

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

# Tag Archives: 05C05

## 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