## Proof theory of reflection (1994)

### Cached

### Download Links

- [www.maths.leeds.ac.uk]
- [www.amsta.leeds.ac.uk]
- [maths.leeds.ac.uk]
- [www.amsta.leeds.ac.uk]
- DBLP

### Other Repositories/Bibliography

Venue: | Annals of Pure and Applied Logic |

Citations: | 9 - 1 self |

### BibTeX

@ARTICLE{Rathjen94prooftheory,

author = {Michael Rathjen},

title = {Proof theory of reflection},

journal = {Annals of Pure and Applied Logic},

year = {1994},

volume = {68},

pages = {181--224}

}

### OpenURL

### Abstract

The paper contains proof–theoretic investigations on extensions of Kripke–Platek set theory, KP, which accommodate first order reflection. Ordinal analyses for such theories are obtained by devising cut elimination procedures for infinitary calculi of ramified set theory with Πn reflection rules. This leads to consistency proofs for the theories KP + Πn–reflection using a small amount of arithmetic (PRA) and the well–foundedness of a certain ordinal notation system with respect to primitive recursive descending sequences. Regarding future work, we intend to avail ourselves of these new cut elimination techniques to attain an ordinal analysis of Π 1 2 comprehension by approaching Π1 2 comprehension through transfinite levels of reflection. 1