Fixed point theories and dependent choice

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Archive for Mathematical Logic 39 (7):493-508 (2000)
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Abstract

In this paper we establish the proof-theoretic equivalence of (i) $\hbox {\sf ATR}$ and $\widehat{\hbox{\sf ID}}_{\omega}$ , (ii) $\hbox{\sf ATR}_0+ (\Sigma^1_1-\hbox{\sf DC})$ and $\widehat{\hbox {\sf ID}}_{<\omega^\omega} , and (iii) $\hbox {\sf ATR}+(\Sigma^1_1-\hbox{\sf DC})$ and $\widehat{\hbox {\sf ID}}_{<\varepsilon_0} $

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10.1007/s001530050161

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Citations of this work

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Wellordering proofs for metapredicative Mahlo.Thomas Strahm - 2002 - Journal of Symbolic Logic 67 (1):260-278.
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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Reflecting on incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.
On the relationship between ATR 0 and.Jeremy Avigad - 1996 - Journal of Symbolic Logic 61 (3):768-779.

View all 6 references / Add more references