Editing Mathematical logic (section)

==Connections with computer science==
{{Main|Logic in computer science}}
The study of [[computability theory (computer science)|computability theory in computer science]] is closely related to the study of computability in mathematical logic.  There is a difference of emphasis, however.  [[Computer science|Computer scientists]] often focus on concrete programming languages and [[feasible computability]], while researchers in mathematical logic often focus on computability as a theoretical concept and on noncomputability.

The theory of [[Program semantics|semantics of programming languages]] is related to [[model theory]], as is [[program verification]] (in particular, [[model checking]]). The [[Curry–Howard correspondence]] between proofs and programs relates to [[proof theory]], especially [[intuitionistic logic]]. Formal calculi such as the [[lambda calculus]] and [[combinatory logic]] are now studied as idealized [[programming languages]].

Computer science also contributes to mathematics by developing techniques for the automatic checking or even finding of proofs, such as [[automated theorem proving]] and [[logic programming]].

[[Descriptive complexity theory]] relates logics to [[Computational complexity theory|computational complexity]]. The first significant result in this area, [[Fagin's theorem]] (1974) established that [[NP (complexity)|NP]] is precisely the set of languages expressible by sentences of existential [[second-order logic]].