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Mathematical logic

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{{for|Quine's theory sometimes called "Mathematical Logic"|New Foundations}}
{{redirect|Mathematical formalism|the philosophical view|Formalism (philosophy of mathematics)}}
'''Mathematical logic''' is a subfield of [[mathematics]] exploring the applications of formal [[logic]] to mathematics awesome.. It bears close connections to [[metamathematics]], the [[foundations of mathematics]], and [[theoretical computer science]].<ref>Undergraduate texts include Boolos, Burgess, and Jeffrey [[#CITEREFBoolosBurgessJeffrey2002|(2002)]], [[Herbert Enderton|Enderton]] [[#CITEREFEnderton2001|(2001)]], and Mendelson [[#CITEREFMendelson1997|(1997)]]. A classic graduate text by Shoenfield [[#CITEREFShoenfield2001|(2001)]] first appeared in 1967.</ref> The unifying themes in mathematical logic include the study of the expressive power of [[formal system]]s and the [[Deductive reasoning|deductive]] power of formal [[Mathematical proof|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 [[definable set|definability]]. In computer science (particularly in the [[ACM Computing Classification System|ACM Classification]]) mathematical logic encompasses additional topics not detailed in this article; see [[Logic in computer science]] for those.
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