| Title:
|
Forcing in the alternative set theory. II (English) |
| Author:
|
Sgall, Jiří |
| Author:
|
Sochor, Antonín |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
339-353 |
| . |
| Category:
|
math |
| . |
| Summary:
|
By the technique of forcing, some new independence results are proved for the alternative set theory (AST) and similar weak theories: The scheme of choice is independent both of AST and of second order arithmetic, axiom of constructibility is independent of AST plus schemes of choice. (English) |
| Keyword:
|
alternative set theory |
| Keyword:
|
second order arithmetic |
| Keyword:
|
forcing |
| Keyword:
|
schemes of choice |
| Keyword:
|
axiom of constructibility |
| Keyword:
|
degrees of constructibility |
| MSC:
|
03E25 |
| MSC:
|
03E35 |
| MSC:
|
03E40 |
| MSC:
|
03E45 |
| MSC:
|
03E70 |
| idZBL:
|
Zbl 0751.03026 |
| idMR:
|
MR1137795 |
| . |
| Date available:
|
2009-01-08T17:44:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116975 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/116974 |
| . |
| Reference:
|
[A] Adamowicz Z.: Constructible semi-lattices of degrees of constructibility.In: Set Theory and Hierarchy Theory V, Lecture Notes in Mathematics 619, p. 1-43. Zbl 0369.02042, MR 0505487 |
| Reference:
|
[L] Lévy A.: Definability in axiomatic set theory II.In: Mathematical Logic and Foundations of Set Theory, ed. by Y. Bar-Hillel, North-Holland, 1970. MR 0268037 |
| Reference:
|
[S 1982] Sochor A.: Metamathematics of the alternative set theory II.Comment. Math. Univ. Carolinae 23 (1982), 55-79. Zbl 0493.03030, MR 0653351 |
| Reference:
|
[S 1985] Sochor A.: Constructibility and shiftings of view.Comment. Math. Univ. Carolinae 26 (1985), 477-498. Zbl 0583.03040, MR 0817822 |
| Reference:
|
[Sg] Sgall J.: Forcing in the alternative set theory I.Comment. Math. Univ. Carolinae 32 (1991), 323-337. Zbl 0751.03025, MR 1137794 |
| Reference:
|
[V] Vopěnka P.: Mathematics in the Alternative Set Theory.Leipzig, 1979. MR 0581368 |
| . |
