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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

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