# The omega-rule interpretation of transfinite provability logic

@article{FernndezDuque2018TheOI, title={The omega-rule interpretation of transfinite provability logic}, author={David Fern{\'a}ndez-Duque and Joost J. Joosten}, journal={Ann. Pure Appl. Log.}, year={2018}, volume={169}, pages={333-371} }

## Figures from this paper

## 17 Citations

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### A Self-contained Provability Calculus for Γ0

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Since the order between these notations can be established in terms of derivability within the calculus, the inferences in this system can be carried out without using any external property of ordinals.

### Hyperarithmetical Worm Battles

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It is shown that indeed the natural transfinite extension of GLP is sound for this interpretation, and yields independent combinatorial principles for the second order theory ACA of arithmetical comprehension with full induction.

### Arithmetical and Hyperarithmetical Worm Battles

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. Japaridze’s provability logic GLP has one modality [ n ] for each natural number and has been used by Beklemishev for a proof theoretic analysis of Peano aritmetic ( PA ) and related theories.…

### MÜNCHHAUSEN PROVABILITY

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The paper exploits the fact that provability is complete and that similar results hold for stronger provability notions, and proves soundness and completeness for the proposed interpretation for a wide class of theories, namely for any theory that can formalise the recursion described above and that has some further very natural properties.

### Derived topologies on ordinals and stationary reflection

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We study the transfinite sequence of topologies on the ordinal numbers that is obtained through successive closure under Cantor’s derivative operator on sets of ordinals, starting form the usual…

### Topological Completeness of the Transfinite Provability Logic

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Let $\Lambda$ be an ordinal. The polymodal provability logic GLP$_\Lambda$ contains modalities $\langle\lambda\rangle$ for $\lambda < \Lambda$ intended to capture progressively stronger notions of…

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