Subrecursive degrees and fragments of Peano Arithmetic

2001 ◽  
Vol 40 (5) ◽  
pp. 365-397 ◽  
Author(s):  
Lars Kristiansen
Keyword(s):  
Peano Arithmetic ◽  
Fragments Of Peano Arithmetic

Friedberg Numbering in Fragments of Peano Arithmetic and α-Recursion Theory

2013 ◽  
Vol 78 (4) ◽  
pp. 1135-1163 ◽  
Author(s):  
Wei Li
Keyword(s):  
Recursion Theory ◽  
Peano Arithmetic ◽  
Fragments Of Peano Arithmetic

AbstractIn this paper, we investigate the existence of a Friedberg numbering in fragments of Peano Arithmetic and initial segments of Gödel's constructible hierarchy Lα, where α is Σ1 admissible. We prove that(1) Over P− + BΣ2, the existence of a Friedberg numbering is equivalent to IΣ2, and(2) For Lα, there is a Friedberg numbering if and only if the tame Σ2 projectum of α equals the Σ2 cofinality of α.

scholarly journals Maximal sets and fragments of Peano arithmetic

1989 ◽  
Vol 115 ◽  
pp. 165-183 ◽  
Author(s):  
C.T. Chong
Keyword(s):  
Recursion Theory ◽  
Peano Arithmetic ◽  
Base Theory ◽  
Abstract Principle ◽  
Priority Method ◽  
General Program ◽  
Fragments Of Peano Arithmetic

This work is inspired by the recent paper of Mytilinaios and Slaman [9] on the infinite injury priority method. It may be considered to fall within the general program of the study of reverse recursion theory: What axioms of Peano arithmetic are required or sufficient to prove theorems in recursion theory? Previous contributions to this program, especially with respect to the finite and infinite injury priority methods, can be found in the works of Groszek and Mytilinaios [4], Groszek and Slaman [5], Mytilinaios [8], Slaman and Woodin [10]. Results of [4] and [9], for example, together pinpoint the existence of an incomplete, nonlow r.e. degree to be provable only within some fragment of Peano arithmetic at least as strong as P- + IΣ2. Indeed an abstract principle on infinite strategies, such as that on the construction of an incomplete high r.e. degree, was introduced in [4] and shown to be equivalent to Σ2 induction over the base theory P- + IΣ0 of Peano arithmetic.

scholarly journals The minimal e-degree problem in fragments of Peano arithmetic

2005 ◽  
Vol 131 (1-3) ◽  
pp. 159-175
Author(s):  
M.M. Arslanov ◽  
C.T. Chong ◽  
S.B. Cooper ◽  
Y. Yang
Keyword(s):  
Peano Arithmetic ◽  
Fragments Of Peano Arithmetic
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