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Mathematical logic
Mathematical logic
is a subfield of
mathematics
exploring the applications of formal
logic
to mathematics. It bears close connections to
metamathematics
, the
foundations of mathematics
, and
theoretical computer science
. The unifying themes in mathematical logic include the study of the expressive power of
formal systems
and the
deductive
power of formal
proof
systems. Mathematical logic is often divided into the fields of
set theory
,
model theory
,
recursion theory
, and
proof theory
. These areas share basic results on logic, particularly
first-order logic
, and
definability
. In computer science (particularly in the
ACM Classification
) mathematical logic encompasses additional topics not detailed in this article; see
Logic in computer science
for those.
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