## Journal of Symbolic Logic

### Friedberg numbering in fragments of Peano Arithmetic and $\alpha$-recursion theory

Wei Li

#### Abstract

In this paper, we investigate the existence of a Friedberg numbering in fragments of Peano Arithmetic and initial segments of Gödel's constructible hierarchy $L_\alpha$, where $\alpha$ is $\Sigma_1$ admissible. We prove that

(1) Over $P^-+B\Sigma_2$, the existence of a Friedberg numbering is equivalent to $I\Sigma_2$, and

(2) For $L_\alpha$, there is a Friedberg numbering if and only if the tame $\Sigma_2$ projectum of $\alpha$ equals the $\Sigma_2$ cofinality of $\alpha$.

#### Article information

Source
J. Symbolic Logic Volume 78, Issue 4 (2013), 1135-1163.

Dates
First available in Project Euclid: 5 January 2014

https://projecteuclid.org/euclid.jsl/1388953997

Digital Object Identifier
doi:10.2178/jsl.7804060

Mathematical Reviews number (MathSciNet)
MR3156515

Zentralblatt MATH identifier
1349.03084

#### Citation

Li, Wei. Friedberg numbering in fragments of Peano Arithmetic and $\alpha$-recursion theory. J. Symbolic Logic 78 (2013), no. 4, 1135--1163. doi:10.2178/jsl.7804060. https://projecteuclid.org/euclid.jsl/1388953997