Fixed points and self-reference
It is shown how Gödel's famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. The abstract fixed point theorem of this article is independent of both metamathematics and recursion theory and is perfectly comprehensible to the non-specia...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000296 |
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| _version_ | 1832558576183279616 |
|---|---|
| author | Raymond M. Smullyan |
| author_facet | Raymond M. Smullyan |
| author_sort | Raymond M. Smullyan |
| collection | DOAJ |
| description | It is shown how Gödel's famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. The abstract fixed point theorem of this article is independent of both metamathematics and recursion theory and is perfectly comprehensible to the non-specialist. |
| format | Article |
| id | doaj-art-31c57811fed24d1da945378ab08d5153 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-31c57811fed24d1da945378ab08d51532025-02-03T01:32:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017228328910.1155/S0161171284000296Fixed points and self-referenceRaymond M. Smullyan0Department of Philosophy, Indiana University, Bloomington 47405, Indiana, USAIt is shown how Gödel's famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. The abstract fixed point theorem of this article is independent of both metamathematics and recursion theory and is perfectly comprehensible to the non-specialist.http://dx.doi.org/10.1155/S0161171284000296diagonalizationfixed pointself referenceequivalence relation. |
| spellingShingle | Raymond M. Smullyan Fixed points and self-reference International Journal of Mathematics and Mathematical Sciences diagonalization fixed point self reference equivalence relation. |
| title | Fixed points and self-reference |
| title_full | Fixed points and self-reference |
| title_fullStr | Fixed points and self-reference |
| title_full_unstemmed | Fixed points and self-reference |
| title_short | Fixed points and self-reference |
| title_sort | fixed points and self reference |
| topic | diagonalization fixed point self reference equivalence relation. |
| url | http://dx.doi.org/10.1155/S0161171284000296 |
| work_keys_str_mv | AT raymondmsmullyan fixedpointsandselfreference |