Transreal proof of the existence of universal possible worlds

Gomide, W., dos Reis, T. S. and Anderson, J. (2015) Transreal proof of the existence of universal possible worlds. In: Unilog 2015 - 5th World Congress and School on Universal Logic, June 25-30, 2015., Instanbul, Turkey, p. 324. (Handbook of the 5th World Congress and School on Universal Logic Instanbul, Turkey)

Abstract/Summary

Transreal arithmetic is total, in the sense that the fundamental operations of addition, subtraction, multiplication and division can be applied to any transreal numbers with the result being a transreal number [1]. In particular division by zero is allowed. It is proved, in [3], that transreal arithmetic is consistent and contains real arithmetic. The entire set of transreal numbers is a total semantics that models all of the semantic values, that is truth values, commonly used in logics, such as the classical, dialetheaic, fuzzy and gap values [2]. By virtue of the totality of transreal arithmetic, these logics can be implemented using total, arithmetical functions, specifically operators, whose domain and counterdomain is the entire set of transreal numbers