CZF and second order arithmetic

DOI10.1016/j.apal.2005.07.002zbMath1094.03038arXiv1510.00469OpenAlexW2963504323MaRDI QIDQ2498896

Robert S. Lubarsky

Publication date: 16 August 2006

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.00469

zbMATH Keywords

intuitionistic set theoryrecursive realizabilityequiconsistency

Mathematics Subject Classification ID

Nonclassical and second-order set theories (03E70) Second- and higher-order arithmetic and fragments (03F35) Intuitionistic mathematics (03F55)

Related Items (11)

On Tarski’s fixed point theorem ⋮ Topological forcing semantics with settling ⋮ Choice and independence of premise rules in intuitionistic set theory ⋮ Topological inductive definitions ⋮ Extending constructive operational set theory by impredicative principles ⋮ Aspects of predicative algebraic set theory. I: Exact completion ⋮ Aspects of predicative algebraic set theory. II: Realizability ⋮ Independence results around constructive ZF ⋮ Kripke models for subtheories of \textsf{CZF} ⋮ On the existence of Stone-Čech compactification ⋮ Constructive Zermelo-Fraenkel Set Theory, Power Set, and the Calculus of Constructions

Cites Work

• Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
• The strength of some Martin-Löf type theories
• Independence results around constructive ZF
• Metamathematical investigation of intuitionistic arithmetic and analysis. With contributions by C. A. Smorynski, J. I. Zucker and W. A. Howard
• Constructive set theory
• Algebraic set theory and the effective topos
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