The binary expansion and the intermediate value theorem in constructive reverse mathematics

Archive for Mathematical Logic 58 (1-2):203-217 (2019)
Abstract
We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ) is equivalent to weak König lemma ) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \ for convex trees, in the framework of constructive reverse mathematics.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1007/s00153-018-0627-2
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,097
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.
Equivalents of the (Weak) Fan Theorem.Iris Loeb - 2005 - Annals of Pure and Applied Logic 132 (1):51-66.
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.

View all 8 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Classifying Dini's Theorem.Josef Berger & Peter Schuster - 2006 - Notre Dame Journal of Formal Logic 47 (2):253-262.
Constructive Notions of Equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
The Dirac Delta Function in Two Settings of Reverse Mathematics.Sam Sanders & Keita Yokoyama - 2012 - Archive for Mathematical Logic 51 (1-2):99-121.
Reclassifying the Antithesis of Specker's Theorem.Hannes Diener - 2012 - Archive for Mathematical Logic 51 (7-8):687-693.
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.
On the Constructive Notion of Closure Maps.Mohammad Ardeshir & Rasoul Ramezanian - 2012 - Mathematical Logic Quarterly 58 (4-5):348-355.
Reverse-Engineering Reverse Mathematics.Sam Sanders - 2013 - Annals of Pure and Applied Logic 164 (5):528-541.
Reverse Mathematics and a Ramsey-Type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.
A Definitive Constructive Open Mapping Theorem?Douglas Bridges & Hajime Ishihara - 1998 - Mathematical Logic Quarterly 44 (4):545-552.
Unique Solutions.Peter Schuster - 2006 - Mathematical Logic Quarterly 52 (6):534-539.

Analytics

Added to PP index
2018-05-11

Total views
7 ( #685,880 of 2,313,459 )

Recent downloads (6 months)
5 ( #166,853 of 2,313,459 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature