## Tsukuba Journal of Mathematics

- Tsukuba J. Math.
- Volume 22, Number 2 (1998), 305-331.

### Normal forms for derivations in Arai's $AI^{-}_\xi$

#### Abstract

In this paper, we shall consider normal forms for derivations in ${\rm AI}_{\xi}^{-}$, where ${\rm AI}_{\xi}^{-}$ is a system introduced by Arai (cf. [4]) and its consistency implies the consistency of Feferman's ${\rm ID}_{\xi}$ (cf. [6]). We shall give two normal form theorems for derivations in ${\rm AI}_{\xi}^{-}$. One (Theorem 1) implies the consistency of ${\rm AI}_{\xi}^{-}$. The other (Theorem 2) implies the $\omega$-consistency of ${\rm AI}_{\xi}^{-}$.

#### Article information

**Source**

Tsukuba J. Math., Volume 22, Number 2 (1998), 305-331.

**Dates**

First available in Project Euclid: 30 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.tkbjm/1496163583

**Digital Object Identifier**

doi:10.21099/tkbjm/1496163583

**Mathematical Reviews number (MathSciNet)**

MR1650729

**Zentralblatt MATH identifier**

0923.03065

#### Citation

Ikeda, Kazuma. Normal forms for derivations in Arai's $AI^{-}_\xi$. Tsukuba J. Math. 22 (1998), no. 2, 305--331. doi:10.21099/tkbjm/1496163583. https://projecteuclid.org/euclid.tkbjm/1496163583