Classical consequences of continuous choice principles from intuitionistic analysis

DOI10.1215/00294527-2377860zbMath1331.03013arXiv1207.6434OpenAlexW1984505680MaRDI QIDQ2443117

François G. Dorais

Publication date: 4 April 2014

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.6434

zbMATH Keywords

uniformityrealizabilityreverse mathematicsintuitionistic analysissequentialsecond-order arithmeticchoice principlesLifschitz

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35) Subsystems of classical logic (including intuitionistic logic) (03B20) Intuitionistic mathematics (03F55)

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Cites Work

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• Metamathematical investigation of intuitionistic arithmetic and analysis. With contributions by C. A. Smorynski, J. I. Zucker and W. A. Howard
• Reverse mathematics, trichotomy, and dichotomy
• Lifschitz' realizability
• Representations of Reals in Reverse Mathematics
• Applied Proof Theory: Proof Interpretations and Their Use in Mathematics