On Imbedding Operators
Systems are understood to be logical or mathematical logic calculi based on predicate calculus (classical or constructive). An operator 9 revising a formula of the system S1 into a formula of the system S2, is called an imbedding operator from S1 into S2 (see ) if for each formula A of the system S1 the deducibility of the formula A in S1 is equivalent to the deducibility of φ(A)in S2 If every formula of the system S1 is a formula of the system S2 then the imbedding operator φ from S1 into S2 is called regular (see ) if for any formula A of the system S1 the formula A ⊃ φ(A) is deducible in S2 (when all the formulas deducible in S2 are true in a certain interpretation, there results from the regularity of the imbedding operator that it transforms a true formula into a true formula).
KeywordsPredicate Calculus Recursive Function Axiom Schema Positive Entry Arithmetic Formula
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