
related topics 
{math, number, function} 
{theory, work, human} 
{work, book, publish} 
{land, century, early} 
{area, part, region} 
{build, building, house} 

Mathematical logic (also known as symbolic logic) is a subfield of mathematics with close connections to computer science and philosophical logic.^{[1]} The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics. 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 firstorder 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.
Since its inception, mathematical logic has 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 axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, 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, rather than trying to find theories in which all of mathematics can be developed.
Contents
Full article ▸


related documents 
Algorithm 
Emmy Noether 
Natural deduction 
Ordinal number 
Quaternion 
Discrete Fourier transform 
Polynomial 
Regular expression 
Floating point 
Common Lisp 
Eiffel (programming language) 
Prime number 
Surreal number 
Clifford algebra 
Singular value decomposition 
Radix sort 
Generic programming 
Derivative 
Complex number 
Number 
Group (mathematics) 
Smalltalk 
History of mathematics 
Euclidean vector 
Vienna Development Method 
C++ 
Distribution (mathematics) 
Forth (programming language) 
Mandelbrot set 
Binary search algorithm 
