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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

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

# Tag Archives: weak square

## The search for diamonds

Abstract: This is a review I wrote for the Bulletin of Symbolic Logic on the following papers: Saharon Shelah, Middle Diamond, Archive for Mathematical Logic, vol. 44 (2005), pp. 527–560. Saharon Shelah, Diamonds, Proceedings of the American Mathematical Society, vol. … Continue reading

Posted in Publications, Reviews, Squares and Diamonds
Tagged Diamond, middle diamond, weak diamond, weak square
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## A cofinality-preserving small forcing may introduce a special Aronszajn tree

Extended Abstract: Shelah proved that Cohen forcing introduces a Souslin tree; Jensen proved that a c.c.c. forcing may consistently add a Kurepa tree; Todorcevic proved that a Knaster poset may already force the Kurepa hypothesis; Irrgang introduced a c.c.c. notion … Continue reading

Posted in Publications, Squares and Diamonds
Tagged 03E04, 03E05, 03E35, Aronszajn tree, Small forcing, Successor of Singular Cardinal, weak square
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## Young Researchers in Set Theory, March 2011

These are the slides of a talk I gave at the Young Researchers in Set Theory 2011 meeting (Königswinter, 21–25 March 2011). Talk Title: Around Jensen’s square principle Abstract: Jensen‘s square principle for a cardinal $\lambda$ asserts the existence of a particular ladder … Continue reading