Bezkwantyfikatorowy rachunek nazw z regułą ekstensjonalności

Ludwik Borkowski has constructed a quantifier-less calculus of names (BRN1), which is regarded as a base system here. The system can be extended with the use of the deductive power of rules of introduction and omission of functors π and σ (BRN2), which serve here as the substitutes of quantifiers. If we adopt the extensionality rule for the functor of singular inclusion (REε), we obtain yet another extending of the system (BRN3) accompanied by simultaneous considerable reduction of the primary rules. The interpretation of the last system in elementary ontology is included.