### 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

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

# 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