83 research outputs found
The proof-theoretic analysis of transfinitely iterated fixed point theories
This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories and ; the exact proof-theoretic ordinals of these systems are presente
The proof-theoretic analysis of transfinitely iterated quasi least fixed points
The starting point of this article is an old question asked by Feferman in his paper on Hancock's conjecture [6] about the strength of . This theory is obtained from the well-known theory ID1 by restricting fixed point induction to formulas that contain fixed point constants only positively. The techniques used to perform the proof-theoretic analysis of also permit to analyze its transfinitely iterated variants . Thus, we eventually know tha
Intuitionistic fixed point theories over Heyting arithmetic
In this paper we show that an intuitionistic theory for fixed points is
conservative over the Heyting arithmetic with respect to a certain class of
formulas. This extends partly the result of mine. The proof is inspired by the
quick cut-elimination due to G. Mints
Functional interpretation and inductive definitions
Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional
interpretation of classical theories of positive arithmetic inductive
definitions, reducing them to theories of finite-type functionals defined using
transfinite recursion on well-founded trees.Comment: minor corrections and change
Upper bounds for metapredicative Mahlo in explicit mathematics and admissible set theory
In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are established
Upper bounds for metapredicative Mahlo in explicit mathematics and admissible set theory
In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are establishe
Transfinite dependent choice and ω-model reflection
In this paper we present some metapredicative subsystems of analysis. We deal with reflection principles, ω-model existence axioms (limit axioms) and axioms asserting the existence of hierarchies. We show several equivalences among the introduced subsystems. In particular we prove the equivalence of Σ1 1 transfinite dependent choice and Π2 1 reflection on ω-models of Σ1 1-D
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