Functions and Analysis

    

Set Theory NC_{∞^{}}^{} Based on Bivalent Infinitary Logic with Restricted Modus Ponens Rule. Basic Real Analysis on External Non-Archimedean Field ℝ_{c}^{}. Basic Complecs Analysis on External Field ℂ_{c}^{}=ℝ_{c}^{}[i].

Authors: Jaykov Foukzon

In this paper we deal with set theory NC_{∞}^{} based on gyper infinitary logic with Restricted Modus Ponens Rule [1]-[3].The main goal of this paper is to present basic analysis on external non Archimedean field ℝ_{c}^{}.The non Archimedean external field ℝ_{c}^{} consist of Cauchy hyperreals.The non-Archimedean external field ℝ_{c}^{#}≠┊^{∗}ℝ┊ is obtained as generalized Cauchy completion of non-Archimedean field ℚ^{#} or ^{∗}ℚ.In order to obtain such completion we deal with external hyper infinite Cauchy sequences {x_{n}}_{n∈ℕ^{#}},{x_{n}}_{n∈┊^{∗}ℕ┊}.We have emphasised that such external Cauchy sequences defined external hyperreal numbers in natural way. Basic Analysis on External Non-Archimedean Field ℝ_{c}^{#} is considered.

Comments: 132 Pages.

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Submission history

[v1] 2021-11-27 16:26:39
[v2] 2021-12-19 01:34:57

Unique-IP document downloads: 484 times

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