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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

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

# 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