Abstract
In this paper we show that the lengths of the approximating processes in epsilon substitution method are calculable by ordinal recursions in an optimal way.
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Arai T.: Epsilon substitution method for theories of jump hierachies. Arch. Math. Logic 41, 123–153 (2002)
Arai T.: Epsilon substitution method for \({ID_{1}(\Pi^{0}_{1}\lor\Sigma_{1}^{0})}\). Ann. Pure Appl. Logic 121, 163–208 (2003)
Arai, T.: An expository survey on epsilon substitution method. In: Proceedings of the Asian Mathematical Congress, Singapore (2005)
Arai T.: Epsilon substitution method for \({[\Pi^{0}_{1},\Pi^{0}_{1}]}\)-FIX. Arch. Math. Logic 44, 1009–1043 (2005)
Arai T.: Ideas in the epsilon substitution method for \({\Pi^{0}_{1}}\)-FIX. Ann. Pure Appl. Logic 136, 3–21 (2005)
Arai T.: Epsilon substitution method for \({\Pi^{0}_{2}}\)-FIX. J. Symb. Logic 71, 1155–1188 (2006)
Tait W.W.: Nested recursion. Math. Ann. 143, 236–250 (1961)
Tait W.W.: Functionals defined by transfinite recursion. J. Symb. Logic 30, 155–174 (1965)
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Arai, T. Exact bounds on epsilon processes. Arch. Math. Logic 50, 445–458 (2011). https://doi.org/10.1007/s00153-010-0225-4
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DOI: https://doi.org/10.1007/s00153-010-0225-4