### 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

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

# 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