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Slow reflection.
- Source :
-
Annals of Pure & Applied Logic . Dec2017, Vol. 168 Issue 12, p2103-2128. 26p. - Publication Year :
- 2017
-
Abstract
- We describe a “slow” version of the hierarchy of uniform reflection principles over Peano Arithmetic ( PA ). These principles are unprovable in Peano Arithmetic (even when extended by usual reflection principles of lower complexity) and introduce a new provably total function. At the same time the consistency of PA plus slow reflection is provable in PA + Con ( PA ) . We deduce a conjecture of S.-D. Friedman, Rathjen and Weiermann: Transfinite iterations of slow consistency generate a hierarchy of precisely ε 0 stages between PA and PA + Con ( PA ) (where Con ( PA ) refers to the usual consistency statement). [ABSTRACT FROM AUTHOR]
- Subjects :
- *HIERARCHY (Linguistics)
*ITERATED integrals
*ARITHMETIC
*TRANSFINITE numbers
Subjects
Details
- Language :
- English
- ISSN :
- 01680072
- Volume :
- 168
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Annals of Pure & Applied Logic
- Publication Type :
- Academic Journal
- Accession number :
- 125415967
- Full Text :
- https://doi.org/10.1016/j.apal.2017.06.003