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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
- Genearlizations 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

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

# 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