| Title:
|
Dependences between definitions of finiteness (English) |
| Author:
|
Spišiak, Ladislav |
| Author:
|
Vojtáš, Peter |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1988 |
| Pages:
|
389-397 |
| . |
| Category:
|
math |
| . |
| MSC:
|
03E25 |
| MSC:
|
03E30 |
| idZBL:
|
Zbl 0667.03040 |
| idMR:
|
MR950292 |
| DOI:
|
10.21136/CMJ.1988.102234 |
| . |
| Date available:
|
2008-06-09T15:21:55Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102234 |
| . |
| Reference:
|
[1] A. Blass: Existence of bases implies the axiom of choice.In J. E. Baumgartner, D. A. Martin, S. Shelah editors. Axiom. Set Theory. Contemporary Mathematics 31 (1984) 31 - 33. Zbl 0557.03030, MR 0763890, 10.1090/conm/031/763890 |
| Reference:
|
[2] J. D. Halpern P. E. Howard: Cardinals m such that 2m = m.Proc. Amer. Math. Soc. 26 (1970) 487-490. MR 0268034 |
| Reference:
|
[3] J. D. Halpern P. E. Howard: Cardinal addition and the Axiom of Choice.Bull. Amer. Math. Soc. 80 (1974) 584-586. MR 0329890, 10.1090/S0002-9904-1974-13510-X |
| Reference:
|
[4] T. Jech: Eine Bemerkung zum Auswahlaxiom.Časopis Pěst. Mat. 93 (1968), 30-31. Zbl 0167.27402, MR 0233706 |
| Reference:
|
[5] T. Jech: The Axiom of Choice.Studies in Logic and the Foundation of Mathematics 75, North Holland, Amsterdam 1973. Zbl 0259.02052, MR 0396271 |
| Reference:
|
[6] T. Jech A. Sochor: Applications of the $\Theta$-model.Bull. Acad. Polon. Sci. 16 (1966) 351-355. MR 0228337 |
| Reference:
|
[7] A. Levy: The independence of various definitions of finiteness.Fund. Math. XLVI (1958) 1-13. Zbl 0089.00702, MR 0098671 |
| Reference:
|
[8] A. Levy: Basic Set Theory. $\Omega$ Perspectives in Mathematical Logic.Springer-Verlag 1979. MR 0533962 |
| Reference:
|
[9] A. R. D. Mathias: Surrealistic landscape with figures (a survey of recent results in set theory).Periodica Math. Hungarica 10 (1979) 109-175. MR 0539225, 10.1007/BF02025889 |
| Reference:
|
[10] G. Sageev: An independence result concerning the Axiom of Choice.Ann. Math. Logic 8(1975) 1-184. Zbl 0306.02060, MR 0366668, 10.1016/0003-4843(75)90002-9 |
| Reference:
|
[11] G. Sageev: A model of ZF in which the Dedekind cardinals constitute a natural nonstandard model of Arithmetic.To appear. |
| Reference:
|
[12] W. Sierpinski: Cardinal and ordinal numbers.PWN, Warszawa 1958. Zbl 0083.26803, MR 0095787 |
| Reference:
|
[13] L. Spišiak: Definitions of finiteness.To appear. |
| Reference:
|
[14] A. Tarski: Sur quelques théorèmes qui équivalent a l'axiome du choix.Fund. Math. 5 (1924) 147-154. 10.4064/fm-5-1-147-154 |
| Reference:
|
[15] A. Tarski: Sur les ensembles finis.Fund. Math. 6 (1924) 45-95. 10.4064/fm-6-1-45-95 |
| Reference:
|
[16] J. Truss: Classes of Dedekind finite cardinals.Fund. Math. To appear. Zbl 0292.02049, MR 0469760 |
| . |
