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  1. Epsilon Substitution Method for [Image] -FIX.Toshiyasu Arai - 2006 - Journal of Symbolic Logic 71 (4):1155 - 1188.
    In this paper we formulate epsilon substitution method for a theory $\Pi _{2}^{0}$-FIX for non-monotonic $\Pi _{2}^{0}$ inductive definitions. Then we give a termination proof of the H-processes based on Ackermann [1].
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  • Exact Bounds on Epsilon Processes.Toshiyasu Arai - 2011 - Archive for Mathematical Logic 50 (3-4):445-458.
    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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