A study of singular points and supports of measures in reverse mathematics

Annals of Pure and Applied Logic 79 (2):211-219 (1996)
  Copy   BIBTEX

Abstract

Arithmetical comprehension is proved to be equivalent to the enumerability of singular points of any measure on the Cantor space. It is provable in ACA0 that any perfect closed subset of [0, 1] is the support of some continuous positive linear functional on C[0, 1]

Categories

Keywords

Reprint years

DOI

10.1016/0168-0072(95)00042-9

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

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

Through your library

My notes

Similar books and articles

The Dirac delta function in two settings of Reverse Mathematics.Sam Sanders & Keita Yokoyama - 2012 - Archive for Mathematical Logic 51 (1-2):99-121.
Strict reverse mathematics draft.Harvey M. Friedman - unknown
Questioning Constructive Reverse Mathematics.I. Loeb - 2012 - Constructivist Foundations 7 (2):131-140.
Open questions in reverse mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Reverse mathematics: the playground of logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.
Lebesgue Convergence Theorems and Reverse Mathematics.Xiaokang Yu - 1994 - Mathematical Logic Quarterly 40 (1):1-13.
Reverse mathematics of separably closed sets.Jeffry L. Hirst - 2006 - Archive for Mathematical Logic 45 (1):1-2.
Undecidable theories and reverse mathematics.James H. Schmerl - 2005 - In Stephen Simpson (ed.), Reverse Mathematics 2001. pp. 21--349.
Free sets and reverse mathematics.Carl G. Jockusch Jr - 2005 - In Stephen Simpson (ed.), Reverse Mathematics 2001. pp. 104.
Interval Orders and Reverse Mathematics.Alberto Marcone - 2007 - Notre Dame Journal of Formal Logic 48 (3):425-448.
Reverse mathematics of prime factorization of ordinals.Jeffry L. Hirst - 1999 - Archive for Mathematical Logic 38 (3):195-201.
Derived sequences and reverse mathematics.Jeffry L. Hirst - 1993 - Mathematical Logic Quarterly 39 (1):447-453.
On the Indecomposability of $\omega^{n}$.Jared R. Corduan & François G. Dorais - 2012 - Notre Dame Journal of Formal Logic 53 (3):373-395.
Reverse Mathematics and Completeness Theorems for Intuitionistic Logic.Takeshi Yamazaki - 2001 - Notre Dame Journal of Formal Logic 42 (3):143-148.
Reverse mathematics and a Ramsey-type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.

Analytics

Added to PP
2014-01-16

Downloads
15 (#923,100)

6 months
7 (#411,886)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Vitali's Theorem and WWKL.Douglas K. Brown, Mariagnese Giusto & Stephen G. Simpson - 2002 - Archive for Mathematical Logic 41 (2):191-206.
Almost everywhere domination.Natasha L. Dobrinen & Stephen G. Simpson - 2004 - Journal of Symbolic Logic 69 (3):914-922.
Mass problems and measure-theoretic regularity.Stephen G. Simpson - 2009 - Bulletin of Symbolic Logic 15 (4):385-409.

Add more citations

References found in this work

Measure theory and weak König's lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.

Add more references