NON-ARCHIMEDEAN FOUNDATIONS OF MATHEMATICS
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Finite foundations of mathematics developed by D. Hilbert are presently considered in computer science as an original mathematical canon. Nevertheless, transfinite foundations of mathematics proposed by G. Cantor can also be urgent for soft computing. In this paper the author considers some perspectives of transfinite foundations, namely he proposes non-Archimedean foundations of mathematics and non-Archimedean multiple-validity. Further, he constructs a logical language with non-Archimedean valued semantics.
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