NON-PRINCIPAL ULTRAFILTERS, PROGRAM EXTRACTION AND HIGHER-ORDER REVERSE MATHEMATICS

DOI10.1142/S021906131250002XzbMath1269.03021arXiv1109.4277MaRDI QIDQ2909619

Alexander P. Kreuzer

Publication date: 6 September 2012

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

Full work available at URL: https://arxiv.org/abs/1109.4277

zbMATH Keywords

program extractionultrafilterconservationfunctional interpretationhigher-order reverse mathematics

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35)

Related Items (5)

Measure theory and higher order arithmetic ⋮ CONSERVATIVITY OF ULTRAFILTERS OVER SUBSYSTEMS OF SECOND ORDER ARITHMETIC ⋮ Logical metatheorems for abstract spaces axiomatized in positive bounded logic ⋮ The Rado path decomposition theorem ⋮ ON IDEMPOTENT ULTRAFILTERS IN HIGHER-ORDER REVERSE MATHEMATICS

Cites Work

• A quantitative version of Kirk's fixed point theorem for asymptotic contractions
• An effective proof that open sets are Ramsey
• Elimination of Skolem functions for monotone formulas in analysis
• Hindman's theorem: an ultrafilter argument in second order arithmetic
• ÜBER EINE BISHER NOCH NICHT BENÜTZTE ERWEITERUNG DES FINITEN STANDPUNKTES
• An Effective Conservation Result for Nonstandard Arithmetic
• On the No-Counterexample Interpretation
• Hindman's theorem, ultrafilters, and reverse mathematics
• Nonstandard Arithmetic and Reverse Mathematics

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