Titlebook: Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum; Symposium Proceeding Peter Schuster,Ulrich Berger,Horst Ossw

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On Conway Numbers and Generalized Real Numbers,fining 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.

HACK

connoisseur

The Points of (Locally) Compact Regular Formal Topologies,gh proved by intuitionistic logic, the result relies on a notion of maximality which contains an impredicative second-order quantification. In this note we present an alternative concept of maximality, entirely phrased in first-order terms, and give a predicative characterization of the points of a

破布

prediabetes

使尴尬

incisive

annexation

Cabinet

,Curt Schmieden’s Approach to Infinitesimals, true for almost all finite natural n. In a paper of 1958 we used rational (and laterreal) sequences to establish a model in which Si was represented by the sequence of the finite natural numbers. Clearly, this approach was less powerful with respect to new applications than Robinson’s (1961) was. Y

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A Sequent Calculus for Constructive Ordered Fields, extended with nonlogical rules. It is proved that structural rules, the rules of cut and contraction in particular, can be eliminated from derivations. The method of extension by nonlogical rules is applied also to the theory of real closed fileds, starting from a quantifier-free axiomatization.