Dependences between definitions of finiteness
Spišiak, Ladislav ; Vojtáš, Peter
Czechoslovak Mathematical Journal, Tome 38 (1988), p. 389-397 / Harvested from Czech Digital Mathematics Library
Publié le : 1988-01-01
Classification:  03E25,  03E30
@article{102234,
     author = {Ladislav Spi\v siak and Peter Vojt\'a\v s},
     title = {Dependences between definitions of finiteness},
     journal = {Czechoslovak Mathematical Journal},
     volume = {38},
     year = {1988},
     pages = {389-397},
     zbl = {0667.03040},
     mrnumber = {950292},
     language = {en},
     url = {http://dml.mathdoc.fr/item/102234}
}
Spišiak, Ladislav; Vojtáš, Peter. Dependences between definitions of finiteness. Czechoslovak Mathematical Journal, Tome 38 (1988) pp. 389-397. http://gdmltest.u-ga.fr/item/102234/

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. (1984) | Article | MR 0763890 | Zbl 0557.03030

J. D. Halpern P. E. Howard Cardinals m such that 2m = m, Proc. Amer. Math. Soc. 26 (1970) 487-490. (1970) | MR 0268034

J. D. Halpern P. E. Howard Cardinal addition and the Axiom of Choice, Bull. Amer. Math. Soc. 80 (1974) 584-586. (1974) | Article | MR 0329890

T. Jech Eine Bemerkung zum Auswahlaxiom, Časopis Pěst. Mat. 93 (1968), 30-31. (1968) | MR 0233706 | Zbl 0167.27402

T. Jech The Axiom of Choice, Studies in Logic and the Foundation of Mathematics 75, North Holland, Amsterdam 1973. (1973) | MR 0396271 | Zbl 0259.02052

T. Jech A. Sochor Applications of the $\Theta$-model, Bull. Acad. Polon. Sci. 16 (1966) 351-355. (1966) | MR 0228337

A. Levy The independence of various definitions of finiteness, Fund. Math. XLVI (1958) 1-13. (1958) | MR 0098671 | Zbl 0089.00702

A. Levy Basic Set Theory. $\Omega$ Perspectives in Mathematical Logic, Springer-Verlag 1979. (1979) | MR 0533962

A. R. D. Mathias Surrealistic landscape with figures (a survey of recent results in set theory), Periodica Math. Hungarica 10 (1979) 109-175. (1979) | Article | MR 0539225

G. Sageev An independence result concerning the Axiom of Choice, Ann. Math. Logic 8(1975) 1-184. (1975) | Article | MR 0366668 | Zbl 0306.02060

G. Sageev A model of ZF in which the Dedekind cardinals constitute a natural nonstandard model of Arithmetic, To appear.

W. Sierpinski Cardinal and ordinal numbers, PWN, Warszawa 1958. (1958) | MR 0095787 | Zbl 0083.26803

L. Spišiak Definitions of finiteness, To appear.

A. Tarski Sur quelques théorèmes qui équivalent a l'axiome du choix, Fund. Math. 5 (1924) 147-154. (1924)

A. Tarski Sur les ensembles finis, Fund. Math. 6 (1924) 45-95. (1924)

J. Truss Classes of Dedekind finite cardinals, Fund. Math. To appear. | MR 0469760 | Zbl 0292.02049