Logical foundations of non—Standard analysis

1981 ◽  
pp. 38-79
Author(s):  
Robert Lutz ◽  
Michel Goze
Keyword(s):  
Standard Analysis ◽  
Logical Foundations ◽  
Non Standard Analysis

scholarly journals Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I)

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2048
Author(s):  
Ileana Ruxandra Badea ◽  
Carmen Elena Mocanu ◽  
Florin F. Nichita ◽  
Ovidiu Păsărescu
Keyword(s):  
Mathematical Modeling ◽  
Artificial Intelligence ◽  
Mathematical Model ◽  
Set Theory ◽  
Standard Analysis ◽  
New Methods ◽  
Internal Set ◽  
Human Thinking ◽  
Global Brain ◽  
Non Standard Analysis

The purpose of this paper is to promote new methods in mathematical modeling inspired by neuroscience—that is consciousness and subconsciousness—with an eye toward artificial intelligence as parts of the global brain. As a mathematical model, we propose topoi and their non-standard enlargements as models, due to the fact that their logic corresponds well to human thinking. For this reason, we built non-standard analysis in a special class of topoi; before now, this existed only in the topos of sets (A. Robinson). Then, we arrive at the pseudo-particles from the title and to a new axiomatics denoted by Intuitionistic Internal Set Theory (IIST); a class of models for it is provided, namely, non-standard enlargements of the previous topoi. We also consider the genetic–epigenetic interplay with a mathematical introduction consisting of a study of the Yang–Baxter equations with new mathematical results.

Zeno’s Paradox from the Paradigms of Standard Analysis and Non-standard Analysis

2018 ◽  
Vol 20 (2) ◽  
pp. 307-318
Author(s):  
Seung Ju Baek ◽  
Young Gi Choi
Keyword(s):  
Standard Analysis ◽  
Non Standard Analysis ◽  
Zeno's Paradox

Non-standard Analysis

2008 ◽  
pp. 1-4
Author(s):  
Peter A. Loeb ◽  
Salim Rashid
Keyword(s):  
Standard Analysis ◽  
Non Standard Analysis
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