A proof-theoretic characterization of the primitive recursive set functions

DOI10.2307/2275441zbMath0761.03016OpenAlexW2088408332MaRDI QIDQ4032873

Michael Rathjen

Publication date: 1 April 1993

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2275441

zbMATH Keywords

Kripke-Platek set theorycut-eliminationprovably recursive functionsprimitive recursive set functionsaxioms of infinity\(\Sigma_ 1\)-foundationsubsystems of KP

Mathematics Subject Classification ID

Cut-elimination and normal-form theorems (03F05) Nonclassical and second-order set theories (03E70) Recursive functions and relations, subrecursive hierarchies (03D20)

Related Items

AN ORDINAL ANALYSIS OF ADMISSIBLE SET THEORY USING RECURSION ON ORDINAL NOTATIONS, Fragments of Kripke-Platek set theory and the metamathematics of \(\alpha \)-recursion theory, End extending models of set theory via power admissible covers, Set-theoretic reflection is equivalent to induction over well-founded classes, Computable aspects of the Bachmann–Howard principle, Interpreting classical theories in constructive ones, Theories and ordinals in proof theory, Logical problems of functional interpretations, A categorical construction of Bachmann–Howard fixed points, Functional interpretation of Aczel's constructive set theory, Predicatively computable functions on sets

Cites Work

• Unnamed Item
• Unnamed Item
• The syntax and semantics of infinitary languages
• On Weak Theories of Sets and Classes which are Based on Strict ∏‐REFLECTION
• The fine structure of the constructible hierarchy