The continuum as a formal space

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Archive for Mathematical Logic 38 (7):423-447 (1999)
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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

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10.1007/s001530050149

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Citations of this work

On constructing completions.Laura Crosilla, Hajime Ishihara & Peter Schuster - 2005 - Journal of Symbolic Logic 70 (3):969-978.

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References found in this work

Intuitionism, an Introduction.A. Heyting - 1958 - Studia Logica 7:277-278.
Constructivism in Mathematics, An Introduction.A. Troelstra & D. Van Dalen - 1991 - Tijdschrift Voor Filosofie 53 (3):569-570.
Topology via Logic.P. T. Johnstone & Steven Vickers - 1991 - Journal of Symbolic Logic 56 (3):1101.
Foundations of Constructive Analysis.Errett Bishop - 1967 - New York, NY, USA: Mcgraw-Hill.

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