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arXiv · 2411.19239

Fibred sets within a predicative and constructive effective topos

Cipriano Junior Cioffo·Maria Emilia Maietti·Samuele Maschio
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Abstract

We describe the fibrational structure of sets within the predicative variant $\mathbf{pEff}$ of Hyland's Effective Topos $\mathbf{Eff}$ previously introduced in Feferman's predicative theory of non-iterative fixpoints $\widehat{ID_1}$. Our structural analysis can be carried out in constructive and predicative variants of $\mathbf{Eff}$ within extensions of Aczel's Constructive Zermelo-Fraenkel Set Theory. All this shows that the full subcategory of discrete objects of Hyland's Effective topos $\mathbf{Eff}$ contains already a fibred predicative topos validating the formal Church's thesis, even when both are formalized in a constructive metatheory.

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Cipriano Junior Cioffo, Maria Emilia Maietti, Samuele Maschio. 2024-12-04. Fibred sets within a predicative and constructive effective topos. https://arxiv.org/abs/2411.19239

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