Skip to main content
SpringerLink
Log in

The continuum as a formal space

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract.

A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Department of Philosophy, P.O. Box 24 (Unioninkatu 40), 00014 University of Helsinki, Helsinki, Finland. e-mail: negri@helsinki.fi , , , , , , FI

    Sara Negri

  2. Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, I-35131 Padova, Italy. e-mail: srvdnl18@stud10.math.unipd.it , , , , , , IT

    Daniele Soravia

Authors
  1. Sara Negri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniele Soravia
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 11 November 1996

Rights and permissions

Reprints and permissions

About this article

Cite this article

Negri, S., Soravia, D. The continuum as a formal space. Arch Math Logic 38, 423–447 (1999). https://doi.org/10.1007/s001530050149

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s001530050149

Search

Navigation