arXiv subjects

Sy Friedman

Publications and source records attributed to Sy Friedman.

2 recordsLinked to original sources

arXiv2019

The Scott rank of Polish metric spaces

We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational $q > 0$, there is a relation $R_{<q}(x,y)$ stating that the distance of $x$ and $y $ is less than $q$. We show that compact spaces have Scott rank at most $\omega$, and that there are discrete ultrametric spaces of arbitrarily high countable Scott rank.

math.MG↗

arXiv2014

Projective measure without projective Baire

We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a $\Delta^1_3$ set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.

math.LO↗