Journal of Symbolic Logic· 2026Q1
FIBRED SETS WITHIN A PREDICATIVE AND CONSTRUCTIVE EFFECTIVE TOPOS
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- 2026year
Short summary
A fibred structure of sets is described within the predicative variant pEff of Hyland's Effective Topos, showing it validates the Formal Church Thesis even in constructive and predicative theories.
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Key points
- Describes the fibrational structure of sets within the predicative Effective Topos (pEff).
- Analysis is extendable to constructive and predicative variants of the Effective Topos (Eff).
- The subcategory of discrete objects in Eff contains a fibred predicative topos.
- This fibred topos validates the Formal Church Thesis under constructive and predicative foundations.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We describe the fibrational structure of sets within the predicative variant pEff $\textbf {pEff}$ bold pEff of Hyland’s Effective Topos Eff ${\mathbf {Eff} }$ bold upper E f f , previously introduced in Feferman’s classical predicative theory of non-iterative fixpoints I D 1 ^ ${\widehat {ID_1}}$ ModifyingAbove upper I upper D 1 With caret . Our structural analysis can be carried out also in constructive and predicative variants of Eff ${\mathbf {Eff} }$ bold upper E f f developed within extensions of Aczel’s constructive Zermelo–Fraenkel set theory. This shows that the full subcategory of discrete objects of Hyland’s Effective Topos Eff ${\mathbf {Eff} }$ bold upper E f f already contains a fibred predicative topos validating the Formal Church Thesis, even when both are formalized in a constructive and predicative foundational theory.
The authors' abstract, as published at the source. Journal of Symbolic Logic, 2026 · DOI ↗
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Field: Management Science and Operations Research
Management Science and Operations ResearchDecision Sciences