| Title:
|
Balcar's theorem on supports (English) |
| Author:
|
Bukovský, Lev |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
443-449 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In A theorem on supports in the theory of semisets [Comment. Math. Univ. Carolinae 14 (1973), no. 1, 1--6] B. Balcar showed that if $\sigma\subseteq D\in M$ is a support, $M$ being an inner model of ZFC, and ${\mathcal P}(D\setminus \sigma)\cap M=r``\sigma$ with $r\in M$, then $r$ determines a preorder "$\preceq$" of $D$ such that $\sigma$ becomes a filter on $(D,\preceq)$ generic over $M$. We show that if the relation $r$ is replaced by a function ${\mathcal P}(D\setminus \sigma)\cap M=f_{-1}(\sigma)$, then there exists an equivalence relation "$\sim$" on $D$ and a partial order on $D/\sim\,$ such that $D/\sim\,$ is a complete Boolean algebra, $\sigma/\sim\,$ is a generic filter and $[f(u)]_{\sim}=-\sum (u/\sim)$ for any $u\subseteq D$, $u\in M$. (English) |
| Keyword:
|
inner model |
| Keyword:
|
support |
| Keyword:
|
generic filter |
| MSC:
|
03E40 |
| idZBL:
|
Zbl 06997361 |
| idMR:
|
MR3914711 |
| DOI:
|
10.14712/1213-7243.2015.266 |
| . |
| Date available:
|
2018-12-28T15:06:58Z |
| Last updated:
|
2021-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147549 |
| . |
| Reference:
|
[1] Balcar B.: A theorem on supports in the theory of semisets.Comment. Math. Univ. Carolinae 14 (1973), no. 1, 1–6. Zbl 0281.02060, MR 0340015 |
| Reference:
|
[2] Balcar B., Štěpánek P.: Set Theory.Academia, Publishing House of the Czechoslovak Academy of Sciences, Praha, 2001 (Czech). MR 0911270 |
| Reference:
|
[3] Jech T.: Set Theory.The Third Millenium Edition, Springer Monographs in Mathematics, Springer, 2003. Zbl 1007.03002, MR 1940513 |
| Reference:
|
[4] Vopěnka P., Hájek P.: The Theory of Semisets.Academia, Publishing House of the Czechoslovak Academy of Sciences, Praha, 1972. Zbl 0332.02064, MR 0444473 |
| . |
