| Title:
|
The smallest common extension of a sequence of models of ZFC (English) |
| Author:
|
Bukovský, Lev |
| Author:
|
Skřivánek, Jaroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
745-752 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note, we show that the model obtained by finite support iteration of a sequence of generic extensions of models of ZFC of length $\omega$ is sometimes the smallest common extension of this sequence and very often it is not. (English) |
| Keyword:
|
model of ZFC |
| Keyword:
|
generic extension |
| Keyword:
|
rigid Boolean algebra |
| Keyword:
|
hereditary $M$-definable |
| MSC:
|
03C62 |
| MSC:
|
03E40 |
| MSC:
|
03E45 |
| idZBL:
|
Zbl 0822.03029 |
| idMR:
|
MR1321245 |
| . |
| Date available:
|
2009-01-08T18:14:54Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118716 |
| . |
| Reference:
|
[1] Blass A.: The model of set generated by countable many generic reals.J. Symbolic Logic 46 (1981), 732-752. MR 0641487 |
| Reference:
|
[2] Bukovský L.: Characterization of generic extensions of models of set theory.Fund. Math. 83 (1973), 35-46. MR 0332477 |
| Reference:
|
[3] Bukovský L.: A general setting of models extensions.International Workshop on Set theory, Abstracts of the talks, Marseilles-Luminy (1990). |
| Reference:
|
[4] Ciesielski K., Guzicki W.: Generic families and models of set theory with the axiom of choice.Proc. Amer. Math. Soc. 106 (1989), 199-206. Zbl 0673.03042, MR 0994389 |
| Reference:
|
[5] Jech T.: Set Theory.Academic Press New York (1978). Zbl 0419.03028, MR 0506523 |
| Reference:
|
[6] Solovay R., Tennenbaum S.: Iterated Cohen Extensions and Souslin`s Problem.Ann. of Math. 94 (1971), 201-245. Zbl 0244.02023, MR 0294139 |
| Reference:
|
[7] Štěpánek P.: Embeddings and automorphisms.Handbook of Boolean algebras J.D. Monk and R. Bonnet North-Holland Amsterdam (1989), 607-635. MR 0991604 |
| Reference:
|
[8] Vopěnka P., Hájek P.: The Theory of Semisets.Academia Prague (1972). MR 0444473 |
| . |
