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A Model in Which the Separation Principle Holds for a Given Effective Projective Sigma-Class

by *,† and *,†
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Oscar Castillo
Axioms 2022, 11(3), 122; https://doi.org/10.3390/axioms11030122
Received: 9 February 2022 / Revised: 22 February 2022 / Accepted: 7 March 2022 / Published: 10 March 2022
(This article belongs to the Section Logic)
In this paper, we prove the following: If n3, there is a generic extension of L—the constructible universe—in which it is true that the Separation principle holds for both effective (lightface) classes Σn1 and Πn1 of sets of integers. The result was announced long ago by Leo Harrington with a sketch of the proof for n=3; its full proof has never been presented. Our methods are based on a countable product of almost-disjoint forcing notions independent in the sense of Jensen–Solovay. View Full-Text
Keywords: separation; projective hierarchy; forcing separation; projective hierarchy; forcing
MDPI and ACS Style

Kanovei, V.; Lyubetsky, V. A Model in Which the Separation Principle Holds for a Given Effective Projective Sigma-Class. Axioms 2022, 11, 122. https://doi.org/10.3390/axioms11030122

AMA Style

Kanovei V, Lyubetsky V. A Model in Which the Separation Principle Holds for a Given Effective Projective Sigma-Class. Axioms. 2022; 11(3):122. https://doi.org/10.3390/axioms11030122

Chicago/Turabian Style

Kanovei, Vladimir, and Vassily Lyubetsky. 2022. "A Model in Which the Separation Principle Holds for a Given Effective Projective Sigma-Class" Axioms 11, no. 3: 122. https://doi.org/10.3390/axioms11030122

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