Unified Foundations for Mathematics
| dc.creator | Burgin, Mark | |
| dc.date | 2004-03-10 | |
| dc.date.accessioned | 2026-07-07T05:06:18Z | |
| dc.date.available | 2026-07-07T05:06:18Z | |
| dc.description | There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole mathematics. Set theory has been for a long time the most popular foundation. However, it was not been able to win completely over its rivals: logic, the theory of algorithms, and theory of categories. Moreover, practical applications of mathematics and its inner problems caused creation of different generalization of sets: multisets, fuzzy sets, rough sets etc. Thus, we encounter a problem: Is it possible to find the most fundamental structure in mathematics? The situation is similar to the quest of physics for the most fundamental "brick" of nature and for a grand unified theory of nature. It is demonstrated that in contrast to physics, which is still in search for a unified theory, in mathematics such a theory exists. It is the theory of named sets. | |
| dc.identifier | https://arxiv.org/abs/math/0403186 | |
| dc.identifier | http://arxiv.org/abs/math/0403186 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70422 | |
| dc.subject | Logic | |
| dc.subject | 03B30 | |
| dc.title | Unified Foundations for Mathematics | |
| dc.type | text |