Swafford, Brenden (2012) Understanding mathematical logic and its applications. Orange Apple, Delhi, India. ISBN 9788132326960
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Abstract
Mathematical logic (also known as symbolic logic) is a subfield of mathematics with close connections to computer science and philosophical logic. 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 first-order logic, and definability. 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 provide 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 providing 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.
| Item Type: | Book |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Electronic Books |
| Depositing User: | Esam @ Hisham Muhammad |
| Date Deposited: | 30 Nov 2022 09:06 |
| Last Modified: | 30 Nov 2022 09:06 |
| URI: | http://odlsystem2.utm.my/id/eprint/3692 |
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