### Archives

### 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

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

# 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
1 Comment

## 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
Leave a comment

## 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