A classification of incompleteness statements
Abstract For which choices of $X,Y,Z\in \{\Sigma ^1_1,\Pi ^1_1\}$ does no sufficiently strong X -sound and Y -definable extension theory prove its own Z -soundness? We give a complete answer, thereby delimiting the generalizations of Gödel’s second incompleteness theorem that hold within second-order arithmetic.
Authors
- James Igoe Walsh (ORCID: https://orcid.org/0000-0002-5833-1705)
- Henry Towsner (ORCID: https://orcid.org/0000-0001-7993-5148)
Institutions
- California University of Pennsylvania (US)
- New York University (US)
- University of Pennsylvania (US)
- Philadelphia University (US)
Publication Details
- Journal
- Canadian Mathematical Bulletin
- Published
- 2025-07-24
- DOI
- https://doi.org/10.4153/s000843952510091x
- Citations
- 1
- Primary Topic
- Logic, Reasoning, and Knowledge
- Type
- article
- Field-Weighted Citation Impact
- 2.48
Funders
- National Science Foundation