Rudin-like sets and hereditary families of compact sets

Abstract

We show that a comeager coanalytic hereditary family of compact sets must have a dense G-delta subfamily which is also hereditary. Using this, we prove an ``abstract'' result which implies the existence of independent M_0 sets and the meagerness of U_0-sets with the property of Baire.

Keywords

• Rudin-like
• hereditary
• families
• compact
• sets