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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

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

# 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
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