On the Π1 1 -separation principle

Mathematical Logic Quarterly 54 (6):563-578 (2008)
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Abstract

We study the proof-theoretic strength of the Π11-separation axiom scheme, and we show that Π11-separation lies strictly in between the Δ11-comprehension and Σ11-choice axiom schemes over RCA0

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10.1002/malq.200710049

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Citations of this work

Transfinite recursion in higher reverse mathematics.Noah Schweber - 2015 - Journal of Symbolic Logic 80 (3):940-969.
The strength of Jullien's indecomposability theorem.Itay Neeman - 2008 - Journal of Mathematical Logic 8 (1):93-119.
The Strength of an Axiom of Finite Choice for Branches in Trees.G. O. H. Jun Le - 2023 - Journal of Symbolic Logic 88 (4):1367-1386.

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References found in this work

Indecomposable linear orderings and hyperarithmetic analysis.Antonio Montalbán - 2006 - Journal of Mathematical Logic 6 (1):89-120.
The Axiom of Choice and the Class of Hyperarithmetic Functions.G. Kreisel - 1970 - Journal of Symbolic Logic 35 (2):333-334.
Forcing with tagged trees.John R. Steel - 1978 - Annals of Mathematical Logic 15 (1):55.
Proof of Mostowski's Conjecture.R. O. Gandy - 1964 - Journal of Symbolic Logic 29 (2):103-104.
Hyperarithmetical Quantifiers.C. Spector & Shih-Chao Liu - 1966 - Journal of Symbolic Logic 31 (1):137-137.

View all 7 references / Add more references