| Autor: |
Cioffo, Cipriano Junior, Maietti, Maria Emilia, Maschio, Samuele |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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