| Title:
|
Generic extensions of models of ZFC (English) |
| Author:
|
Bukovský, Lev |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
347-358 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35--46, saying that for models $M\subseteq N$ of ZFC with same ordinals, the condition $Apr_{M,N}(\kappa)$ implies that $N$ is a $\kappa$-C.C. generic extension of $M$. (English) |
| Keyword:
|
inner model |
| Keyword:
|
extension of an inner model |
| Keyword:
|
$\kappa$-generic extension |
| Keyword:
|
$\kappa$-C.C. generic extension |
| Keyword:
|
$\kappa$-boundedness condition |
| Keyword:
|
$\kappa$ approximation condition |
| Keyword:
|
Boolean ultrapower |
| Keyword:
|
Boolean valued model |
| MSC:
|
03E40 |
| MSC:
|
03E45 |
| idZBL:
|
Zbl 06837070 |
| idMR:
|
MR3708778 |
| DOI:
|
10.14712/1213-7243.2015.209 |
| . |
| Date available:
|
2017-11-22T09:23:21Z |
| Last updated:
|
2019-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146907 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Bukovský L.: Ensembles génériques d'entiers.C.R. Acad. Sci. Paris 273 (1971), 753–755. Zbl 0231.02086, MR 0286647 |
| Reference:
|
[4] Bukovský L.: Characterization of generic extensions of models of set theory.Fund. Math. 83 (1973), 35–46. Zbl 0344.02043, MR 0332477, 10.4064/fm-83-1-35-46 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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[9] Laver R.: Certain very large cardinals are not created in small forcing extensions.Ann. Pure Appl. Logic 149 (2007), 1–6. Zbl 1128.03046, MR 2364192, 10.1016/j.apal.2007.07.002 |
| Reference:
|
[10] Solovay R.: A model of set theory in which every set of reals is Lebesgue measurable.Ann. of Math. 92 (1970), 1–56. Zbl 0207.00905, MR 0265151, 10.2307/1970696 |
| Reference:
|
[11] Vopěnka P.: General theory of $\nabla$-models.Comment. Math. Univ. Carolin. 8 (1967), 145–170. Zbl 0162.01701, MR 0214460 |
| Reference:
|
[12] Vopěnka P., Balcar B.: On complete models of the set theory.Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 839–841. Zbl 0177.01404, MR 0242659 |
| Reference:
|
[13] Vopěnka P., Hájek P.: The Theory of Semisets.Academia, Prague, 1972. Zbl 0332.02064, MR 0444473 |
| . |
