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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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