Wellordering proofs for metapredicative Mahlo
نویسندگان
چکیده
منابع مشابه
Wellordering Proofs for Metapredicative Mahlo
In this article we provide wellordering proofs for metapredicative systems of explicit mathematics and admissible set theory featuring suitable axioms about the Mahloness of the underlying universe of discourse. In particular, it is shown that in the corresponding theories EMA of explicit mathematics and KPm of admissible set theory, transfinite induction along initial segments of the ordinal φ...
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After briefly discussing the concepts of predicativity, metapredicativity and impredicativity, we turn to the notion of Mahloness as it is treated in various contexts. Afterwards the appropriate Mahlo axioms for the framework of explicit mathematics are presented. The article concludes with relating explicit Mahlo to certain nonmonotone inductive definitions. §
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In this article we study the theory KPi + (Σ-TR) which (i) describes a recursively inaccessible universe, (ii) permits the iteration of Σ operations along the ordinals, (iii) does not comprise ∈ induction, and (iv) restricts complete induction on the natural numbers to sets. It is shown that the proof-theoretic ordinal of KPi + (Σ-TR) is the metapredicative Mahlo ordinal φω00. Our system KPi + ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2002
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1190150043