Measure theory and weak König's lemma

Archive for Mathematical Logic 30 (3):171-180 (1990)
  Copy   BIBTEX

Abstract

We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive on open sets

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,419

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Reverse mathematics and a Ramsey-type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.
Weak König's Lemma Implies Brouwer's Fan Theorem: A Direct Proof.Hajime Ishihara - 2006 - Notre Dame Journal of Formal Logic 47 (2):249-252.
The weak König lemma and uniform continuity.Josef Berger - 2008 - Journal of Symbolic Logic 73 (3):933-939.
Separation and weak könig's lemma.A. James Humphreys & Stephen G. Simpson - 1999 - Journal of Symbolic Logic 64 (1):268-278.
A feasible theory for analysis.Fernando Ferreira - 1994 - Journal of Symbolic Logic 59 (3):1001-1011.
Complex analysis in subsystems of second order arithmetic.Keita Yokoyama - 2007 - Archive for Mathematical Logic 46 (1):15-35.
Lebesgue Convergence Theorems and Reverse Mathematics.Xiaokang Yu - 1994 - Mathematical Logic Quarterly 40 (1):1-13.
A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Ramsey’s theorem and König’s Lemma.T. E. Forster & J. K. Truss - 2007 - Archive for Mathematical Logic 46 (1):37-42.
Admissible representations for probability measures.Matthias Schröder - 2007 - Mathematical Logic Quarterly 53 (4):431-445.
On uniform weak König's lemma.Ulrich Kohlenbach - 2002 - Annals of Pure and Applied Logic 114 (1-3):103-116.
How Incomputable Is the Separable Hahn-Banach Theorem?Guido Gherardi & Alberto Marcone - 2009 - Notre Dame Journal of Formal Logic 50 (4):393-425.

Analytics

Added to PP
2013-11-23

Downloads
34 (#346,015)

6 months
4 (#184,953)

Historical graph of downloads
How can I increase my downloads?