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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Received: 18 March 1997
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Jäger, G., Strahm, T. Fixed point theories and dependent choice. Arch Math Logic 39, 493–508 (2000). https://doi.org/10.1007/s001530050161
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DOI: https://doi.org/10.1007/s001530050161