A step semantic system for set theory (Q1065794)

A hierarchy of languages \(M_ n\), for every natural n is constructed, where \(M_ 0\) is the language \(\text{Russian{Ya}}_{\omega}\) of \textit{A. A. Markov} [Dokl. Akad. Nauk. SSSR 214, 1262-1264 (1974; Zbl 0308.02037)]. The hierarchy culminates in a language \(M_{\omega}\) of set theory in constructive mathematics. The truth of various formulas of \(M_{\omega}\) is investigated and it is shown that the language \(M_{\omega}\) is reasonably close to the language of set theory in classical predicate logic.