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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

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

# 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 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