A Normalizing Intuitionistic Set Theory with Inaccessible Sets
نویسندگان
چکیده
منابع مشابه
A Normalizing Intuitionistic Set Theory with Inaccessible Sets
We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs. For this purpose, we axiomatize an impredicative constructive version of Zermelo-Fraenkel set theory IZF with Replacement and ω-many inaccessibles, which we call IZFRω. Our axioma...
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Let us consider two-sorted intuitionistic set theory ZFI2 with sort 0 for natural numbers and sort 1 for sets. We shall show that well-known Church rule with parameters of sort 1 is admissible in ZFI2 in some rather strong sense, and get from this point the admissibility of Markov rule with all parameters in ZFI2, and also DP and numerical EP with set parameters for it in the same sense.
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2007
ISSN: 1860-5974
DOI: 10.2168/lmcs-3(3:6)2007