Research on Set Theory Based on Paraconsistent Logic

Abstract

Different from ZF axiomatic set theory, the paraconsistent set theory has changed the basic logic of set theory and selected paraconsistent logic which can accommodate or deal with contradictions, it effectively avoids the whole theory falling into a non-trivial dilemma when there are contradictions in set theory. In this paper, we first review the history and current situation of the praconsistent set theory; then, we give three kinds of paraconsistent logic which can be used to construct the praconsistent set theory among many kinds of paraconsistent logics. And then, we analyze the differences of methods of the paraconsistent set theory with strong or weak structure of paraconsistent logic and get different paraconsistent set theory. Finally, we verify that paraconsistent set theory is a new method to solve the paradox of set theor. The development of paraconsistent set theory can solve the difficulties in the development of set theory in a unique way, which is not only the extension of the application of paraconsistent logic, but also the new form and new trend of the development of set theory.