Jump to ContentJump to Main Navigation
From Sets and Types to Topology and AnalysisTowards practicable foundations for constructive mathematics$
Users without a subscription are not able to see the full content.

Laura Crosilla and Peter Schuster

Print publication date: 2005

Print ISBN-13: 9780198566519

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566519.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 18 December 2018

CONSTRUCTIVE REVERSE MATHEMATICS: COMPACTNESS PROPERTIES

CONSTRUCTIVE REVERSE MATHEMATICS: COMPACTNESS PROPERTIES

Chapter:
(p.245) 16 CONSTRUCTIVE REVERSE MATHEMATICS: COMPACTNESS PROPERTIES
Source:
From Sets and Types to Topology and Analysis
Author(s):

Hajime Ishihara

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566519.003.0016

This chapter proposes a base formal system for constructive reverse mathematics to classify various theorems in intuitionistic, constructive recursive, and classical mathematics by logical principles, function existence axioms, and their combinations. The system is weak enough to allow for a comparison of the results obtained in it with those obtained within classical reverse mathematics as well as to prove theorems in Bishop's constructive mathematics. The chapter also formalizes results on compactness properties, such as the Heine-Borel theorem, the Cantor intersection theorem, the Bolzano-Weierstrass theorem, and sequential compactness, in the base formal system as test cases of its adequacy and faithfulness for the purpose of constructive reverse mathematics. The computability of function existence axioms and their combination with logical principles are also investigated, identifying them with closure conditions on a class of functions.

Keywords:   constructive mathematics, reverse mathematics, Heine-Borel theorem, Cantor intersection theorem, Bolzano-Weierstrass theorem, sequential compactness

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .