Abstract
John Horton Conway presents in his book “On Numbers and Games” a general method to create a class of numbers containing all real numbers as well as every ordinal number. Using the logical law of excluded middle (LEM) he equips this class with the structure of a totally ordered field. This paper is a first step to investigate the contribution of Conway’s theory to the foundations of Constructive Nonstandard Analysis. In his book Conway suggests defining real numbers as (Conway) cuts in the set of rational numbers. Following his ideas, a constructive notion of real numbers will be developed. Parallels to and differences from the concept of generalized real numbers recently published by Fred Richman [Indag. Mathem., N. S., 9 (4) 595–606 (1998)] will be outlined.
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