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### 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

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

# Tag Archives: Slim tree

## 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 Preprints, 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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