We prove that every strictly positive endofimctor on the category of sets generated by Martin-Liif's extensional type theory has an initial algebra. This representation of inductively defined sets uses essentially the wellorderings introduced by Martin-Liif in "Constructive Mathematics and Computer
The Friedman-Translation for Martin-Löf's Type Theory
✍ Scribed by Erik Palmgren
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 636 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0044-3050
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✦ Synopsis
Abstract
In this note we show that Friedman's syntactic translation for intuitionistic logical systems can be carried over to Martin‐Löf's type theory, inlcuding universes provided some restrictions are made. Using this translation we show that the theory is closed under a higher type version of Markov's rule.
📜 SIMILAR VOLUMES
In the paper there are introduced and discussed the concepts of an indexed category with quantifications and a higher level indexed category to present ~tn algebraic characterization of some version of Martin-L6f Type Theory. This characterization.is given by specifying an additional equational stru