Blurry definability

18.01.2022 15:00 - 16:30

G. Fuchs (City College of New York; US)

In this talk on ongoing research, I analyze blurry forms of ordinal definability and their hereditary versions which generalize ideas due to Hamkins/Leahy and Tzouvaras. Classically, a set is ordinal definable if it is the unique object satisfying some first order property in which ordinal parameters may occur. Given a cardinal kappa, I define that a set is \(<\kappa\)-blurrily ordinal definable if it belongs to an OD set of cardinality less than kappa. So in this case, the set is one of fewer than \(\kappa\) many objects with a certain property using ordinal parameters, not necessarily the unique such set. I will present some results on the class of hereditarily \(<\kappa\)-blurrily definable sets and the structure of leaps, that is, stages at which new sets become blurrily definable. There are some ZF(C) results and some relative consistency results using forcing.

Organiser:

KGRC

Location:
Zoom Meeting