Set theory INC^# based on intuitionistic logic with restricted modus ponens rule

ISBN-13: 9786203925357 / Angielski / Miękka / 60 str.

Jaykov Foukzon

Opis

In this book set theory INC# based on intuitionistic logic with restricted modus ponens rule is proposed. It proved that intuitionistic logic with restricted modus ponens rule can to safe Cantor naive set theory from a triviality Considering only pure sets, the naive set comprehension principle says, for anycondition, that there is a set containing all and only the sets satisfying this condition. Infirst-order logic, this can be formulated as the following schematic principle, where may be any formula in whichy does not occur freely: yxx y . 1.1 Russell's paradox shows that the instance obtained by letting be x x isinconsistent in classical logic. One response to the paradox is to restrict naive setcomprehension by ruling out this and other problematic instances: only for each of somespecial conditions is it claimed there is a set containing all and only the sets satisfyingthe condition.

O autorze

Foukzon, Jaykov Jaykov Foukzon (born October I, 1954). Nationality: Soviet Union. Education: Moscow State University (1976). Doctoral adviser: Lev Pontryagin. Soviet and Russian mathematician and physicist.Institutions: Russian Space Research Institute, Institute of Control Sciences of Russian Academy of Sciences Central Aerohydrodynamic Institute (TsAGI) Russia.