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### 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

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

# 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 Preprints, Singular Cardinals Combinatorics
Tagged HOD, Singular cardinals combinatorics
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