### 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

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

# Tag Archives: HOD

## Ordinal definable subsets of singular cardinals

Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. A remarkable result by Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality then there is a subset $x$ of $\kappa$ such … Continue reading

Posted in Publications, Singular Cardinals Combinatorics
Tagged HOD, Singular cardinals combinatorics
2 Comments