Mathematical Logic

mathematical logic: see symbolic logic.

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mathematical logic [¦math·ə¦mad·ə·kəl ′läj·ik]

(mathematics)

The study of mathematical theories from the viewpoint of model theory, recursive function theory, proof theory, and set theory.

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Mathematical Logic 

a branch of logic that makes use of mathematical methods.

The use of formal languages with an exact syntax and precise semantics that unambiguously define the meaning of formulas is characteristic of mathematical logic. The need for such a logic arose in the early 20th century in connection with the intensive development of the foundations of mathematics, the emergence of set theory in which antinomies had been discovered, the refinement of the concept of an algorithm, as well as with other profound and fundamental problems of mathematical science. The importance of mathematical logic for science as a whole, however, is not exhausted by its mathematical applications, since all sciences require good reasoning and methods of proof. This is why mathematical logic can rightfully be called logic in its most recent development.

A. A. MARKOV