2005•Gongcheng shuxue xuebaoRequires access

On the Strong Completeness of the Formal System L

Daowu Pei

Abstract

General deduction and strong completeness of the formal deductive system L? are further studied. For arbitrary formula set Γ, a kind of new algebraic systems, called R0(Γ) algebras, are proposed. By using some important algebraic tools such as subalgebra, ?lter theory and subdirect product decomposition theory, strong completeness theorem of the system L? is proved.

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Key concepts: Completeness (order theory), Gödel's completeness theorem, Mathematics, Algebraic number, Algebra over a field, Subalgebra, Product (mathematics), Set (abstract data type)