Hyperarithmetic numerals
Caleb M. H. Camrud, Timothy H. McNicholl · arXiv (Cornell University) · 2022
Within the framework of computable infinitary continuous logic, we develop a system of hyperarithmetic numerals. These numerals are infinitary sentences in a metric language $L$ that have the same truth value in every interpretation of $L$. We prove that every hyperarithmetic real can be represented by a hyperarithmetic numeral at the same level of complexity.