## Mathematical logic |

- this article
**has an unclear citation style**.*(july 2019)**(* )learn how and when to remove this template message **mathematical logic**is a subfield of exploring the applications of formalmathematics to mathematics. it bears close connections tologic , themetamathematics , andfoundations of mathematics .theoretical computer science ^{[1]}the unifying themes in mathematical logic include the study of the expressive power of and theformal systems power of formaldeductive systems.proof mathematical logic is often divided into the fields of

,set theory ,model theory , andrecursion theory . these areas share basic results on logic, particularlyproof theory , andfirst-order logic . in computer science (particularly in thedefinability ) mathematical logic encompasses additional topics not detailed in this article; seeacm classification for those.logic in computer science since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics. this study began in the late 19th century with the development of

frameworks foraxiomatic ,geometry , andarithmetic . in the early 20th century it was shaped byanalysis 'sdavid hilbert to prove the consistency of foundational theories. results ofprogram ,kurt gödel , and others provided partial resolution to the program, and clarified the issues involved in proving consistency. work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as ingerhard gentzen ) rather than trying to find theories in which all of mathematics can be developed.reverse mathematics - subfields and scope
- history
- formal logical systems
- set theory
- model theory
- recursion theory
- proof theory and constructive mathematics
- applications
- connections with computer science
- foundations of mathematics
- see also
- notes
- references
- external links

This article has an unclear citation style. (July 2019) ( |

**Mathematical logic** is a subfield of ^{[1]} The unifying themes in mathematical logic include the study of the expressive power of

Mathematical logic is often divided into the fields of

Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics. This study began in the late 19th century with the development of