Basic subtoposes of the effective topos

Annals of Pure and Applied Logic 164 (9):866-883 (2013)

Jaap Van Oosten
Leiden University
We study the lattice of local operators in Hylandʼs Effective Topos. We show that this lattice is a free completion under internal sups indexed by the natural numbers object, generated by what we call basic local operators.We produce many new local operators and we employ a new concept, sight, in order to analyze these.We show that a local operator identified by A.M. Pitts in his thesis, gives a subtopos with classical arithmetic
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DOI 10.1016/j.apal.2013.04.001
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References found in this work BETA

The Medvedev Lattice of Computably Closed Sets.Sebastiaan A. Terwijn - 2006 - Archive for Mathematical Logic 45 (2):179-190.
A Model for Intuitionistic Non-Standard Arithmetic.Ieke Moerdijk - 1995 - Annals of Pure and Applied Logic 73 (1):37-51.
An Omniscience Principle, the König Lemma and the Hahn-Banach Theorem.Hajime Ishihara - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (3):237-240.
Constructive Logic and the Medvedev Lattice.Sebastiaan A. Terwijn - 2006 - Notre Dame Journal of Formal Logic 47 (1):73-82.

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A Kuroda-Style J -Translation.Benno van den Berg - forthcoming - Archive for Mathematical Logic:1-8.

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