| Title:
|
$\in $-representation and set-prolongations (English) |
| Author:
|
Mlček, Josef |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
661-666 |
| . |
| Category:
|
math |
| . |
| Summary:
|
By an $\in $-representation of a relation we mean its isomorphic embedding to $\Bbb E = \{\langle x,y\rangle;\,x\in y\}$. Some theorems on such a representation are presented. Especially, we prove a version of the well-known theorem on isomorphic representation of extensional and well-founded relations in $\Bbb E$, which holds in Zermelo-Fraenkel set theory. This our version is in Zermelo-Fraenkel set theory false. A general theorem on a set-prolongation is proved; it enables us to solve the task of the representation in question. (English) |
| Keyword:
|
isomorphic representation |
| Keyword:
|
extensional relation |
| Keyword:
|
well-founded relation |
| Keyword:
|
set-pro\-lon\-gation |
| MSC:
|
03E70 |
| MSC:
|
04A99 |
| idZBL:
|
Zbl 0784.03032 |
| idMR:
|
MR1240187 |
| . |
| Date available:
|
2009-01-08T17:59:30Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118537 |
| . |
| Reference:
|
[V] Vopěnka P.: Mathematics in the Alternative Set Theory.TEUBNER TEXTE Leipzig (1979). MR 0581368 |
| . |
