Notre Dame J. Formal Logic 64 (1), 15-59, (February 2023) DOI: 10.1215/00294527-2022-0033
KEYWORDS: Gödel phenomena, Incompleteness, recursive functions, representability, core logic, classical core logic, consistency, 1-consistency, ω-consistency, ex falso quodlibet, 03F30, 03F40, 03F52, 03F99, 03B47
This study examines how the Gödel phenomena are to be treated in core logic. We show in formal detail how one can use core logic in the metalanguage to prove Gödel’s incompleteness theorems for arithmetic even when classical logic is used for logical closure in the object language.