On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami

2018/10/30 by Vladimir Kanovei, Kanovei, Vladimir, Vassily Lyubetsky +1 · 1 citation
Computer Science · Mathematics · #03E15 #03E35 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1810.12542

openalex publication_date 2018/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a handwtitten note of 1975, Leo Harrington sketched a construction of a model of ZFC (no large cardinals or anything beyond ZFC!) in which \mathbfΠ¹₃-Separation holds but \mathbfΣ¹₃-Reduction fails. The result has never appeared in a journal or book publication except for a few of old references.

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