Mahlo classes for first-order reflections

Toshiyasu Arai

arXiv:1910.06520·math.LO·October 16, 2019

Mahlo classes for first-order reflections

Toshiyasu Arai

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Abstract

In this note we axiomatize the $Π_{k + 1}$ -consequences in the set theory $KP Π_{N}$ for $Π_{N}$ -reflecting universes in terms of iterations of $Π_{i}$ -recursively Mahlo operations for $1 \leq k \leq i < N$ .

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TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Homotopy and Cohomology in Algebraic Topology