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- Title
Computable aspects of the Bachmann–Howard principle.
- Authors
Freund, Anton
- Abstract
We have previously established that Π 1 1 -comprehension is equivalent to the statement that every dilator has a well-founded Bachmann–Howard fixed point, over A T R 0 . In this paper, we show that the base theory can be lowered to R C A 0 . We also show that the minimal Bachmann–Howard fixed point of a dilator T can be represented by a notation system 𝜗 (T) , which is computable relative to T. The statement that 𝜗 (T) is well founded for any dilator T will still be equivalent to Π 1 1 -comprehension. Thus, the latter is split into the computable transformation T ↦ 𝜗 (T) and a statement about the preservation of well-foundedness, over a system of computable mathematics.
- Subjects
REVERSE mathematics
- Publication
Journal of Mathematical Logic, 2020, Vol 20, Issue 2, pN.PAG
- ISSN
0219-0613
- Publication type
Article
- DOI
10.1142/S0219061320500063