Elementary practice of non standard analysis

Author(s):  
Robert Lutz ◽  
Michel Goze
Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2048
Author(s):  
Ileana Ruxandra Badea ◽  
Carmen Elena Mocanu ◽  
Florin F. Nichita ◽  
Ovidiu Păsărescu

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.


2018 ◽  
Vol 20 (2) ◽  
pp. 307-318
Author(s):  
Seung Ju Baek ◽  
Young Gi Choi

Author(s):  
Peter A. Loeb ◽  
Salim Rashid

1967 ◽  
Vol 74 (5) ◽  
pp. 608
Author(s):  
C. B. Boyer ◽  
A. Robinson ◽  
L. E. J. Brouwer ◽  
A. Heyting ◽  
A. Robinson ◽  
...  

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