Countable ordinals in indiscernibility spectra
Volume 260 / 2023
Fundamenta Mathematicae 260 (2023), 99-109
MSC: Primary 03E10; Secondary 03E15, 03E45, 03F15.
DOI: 10.4064/fm964-6-2022
Published online: 26 September 2022
Abstract
Given a set $A$ of reals, the indiscernibility spectrum of $A$ is the set of countable ordinals which are simultaneously indiscernible in $L[a]$ for every $a^\sharp \in A$. Under large-cardinal assumptions, we construct sets of sharps with countable spectrum, and with spectra of every finite cardinality.
