### Archives

### 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

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

# Category Archives: Reviews

## Review: Stevo Todorcevic’s CRM-Fields-PIMS Prize Lecture

After winning the 2012 CRM-Fields-PIMS Prize, Stevo Todorcevic gave a series of talks on his research: at CRM, at PIMS and at the Fields Institute. The director of the Fields Institute asked me to write a short review on Stevo’s … Continue reading

## Review: Is classical set theory compatible with quantum experiments?

Yesterday, I attended a talk at the Quantum Foundations seminar at the beautiful Perimeter Institute for Theoretical Physics (Waterloo, Ontario). The (somewhat provocative) title of the talk was “Is Classical Set Theory Compatible with Quantum Experiments?”, and the speaker was Radu … Continue reading

## 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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