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  1. Intuitionistic Fixed Point Theories Over Set Theories.Toshiyasu Arai - 2015 - Archive for Mathematical Logic 54 (5-6):531-553.
    In this paper we show that the intuitionistic fixed point theory FiXi over set theories T is a conservative extension of T if T can manipulate finite sequences and has the full foundation schema.
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  • Proof Theory of Weak Compactness.Toshiyasu Arai - 2013 - Journal of Mathematical Logic 13 (1):1350003.
    We show that the existence of a weakly compact cardinal over the Zermelo–Fraenkel's set theory ZF is proof-theoretically reducible to iterations of Mostowski collapsings and Mahlo operations.
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