Hyperarithmetic numerals
Caleb M.H. Camrud, Timothy H. McNicholl
TL;DR
This paper develops a system of hyperarithmetic numerals within computable infinitary continuous logic, showing that every hyperarithmetic real can be represented by such a numeral at the same complexity level.
Contribution
It introduces hyperarithmetic numerals as infinitary sentences in a metric language, linking them to hyperarithmetic reals and their complexity levels.
Findings
Hyperarithmetic numerals are consistent across interpretations.
Every hyperarithmetic real can be represented by a hyperarithmetic numeral.
The complexity of numerals matches that of the real they represent.
Abstract
Within the framework of computable infinitary continuous logic, we develop a system of hyperarithmetic numerals. These numerals are infinitary sentences in a metric language that have the same truth value in every interpretation of . We prove that every hyperarithmetic real can be represented by a hyperarithmetic numeral at the same level of complexity.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Advanced Topology and Set Theory