In this paper we formulate epsilon substitution method for a theory Π⁰₂-FIX for non-monotonic Π⁰₂ inductive definitions. Then we give a termination proof of the H-processes based on Ackermann .
Toshiyasu Arai. "Epsilon substitution method for Π⁰₂-FIX." J. Symbolic Logic 71 (4) 1155 - 1188, December 2006. https://doi.org/10.2178/jsl/1164060450