Abstract
We state the following results: the family of all infinite computably enumerable sets has no computable numbering; the family of all infinite Π11 sets has no Π11 -computable numbering; the family of all infinite Σ21 sets has no Σ21 -computable numbering. For k > 2, the existence of a Σk1 -computable numbering for the family of all infinite Σk1 sets leads to the inconsistency of ZF.
Original language | English |
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Pages (from-to) | 224-231 |
Number of pages | 8 |
Journal | Algebra and Logic |
Volume | 58 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jul 2019 |
Keywords
- analytical hierarchy
- computability
- computable numberings
- Friedberg numbering
- Gödel’s axiom of constructibility
- Godel's axiom of constructibility
- AXIOM