Journal of Symbolic Logic

The proof-theoretic analysis of transfinitely iterated quasi least fixed points

Dieter Probst

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Abstract

The starting point of this article is an old question asked by Feferman in his paper on Hancock’s conjecture [6] about the strength of ID₁*. This theory is obtained from the well-known theory ID₁ by restricting fixed point induction to formulas that contain fixed point constants only positively. The techniques used to perform the proof-theoretic analysis of ID₁* also permit to analyze its transfinitely iterated variants IDα*. Thus, we eventually know that |\hat{ID}α| = |IDα*|.

Article information

Source
J. Symbolic Logic, Volume 71, Issue 3 (2006), 721-746.

Dates
First available in Project Euclid: 4 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1154698573

Digital Object Identifier
doi:10.2178/jsl/1154698573

Mathematical Reviews number (MathSciNet)
MR2250817

Zentralblatt MATH identifier
1115.03084

Keywords
Fixed points Iteration Pseudo-hierarchies

Citation

Probst, Dieter. The proof-theoretic analysis of transfinitely iterated quasi least fixed points. J. Symbolic Logic 71 (2006), no. 3, 721--746. doi:10.2178/jsl/1154698573. https://projecteuclid.org/euclid.jsl/1154698573


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