Dense orderings, partitions and weak forms of choice

• Autorzy: Carlos G. González
• Języki publikacji: EN

Abstrakty

EN

We investigate the relative consistency and independence of statements which imply the existence of various kinds of dense orders, including dense linear orders. We study as well the relationship between these statements and others involving partition properties. Since we work in ZF (i.e. without the Axiom of Choice), we also analyze the role that some weaker forms of AC play in this context

Kategorie tematyczne

• 03E20: Other classical set theory (including functions, relations, and set algebra)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1995
• Tom: 147
• Numer: 1
• Strony: 11-25

Daty

wydano

1995

otrzymano

1993-08-24

poprawiono

1994-10-05

Twórcy

autor

Carlos G. González

• Centro de Lógica, Epistemologia e História da Ciência, Universidade Estadual de Campinas (Unicamp), P.O. Box 6133, 13081-000 Campinas SP, Brazil

Bibliografia

• [1] J. D. Halpern and P. E. Howard, Cardinals m such that 2m = m, Proc. Amer. Math. Soc. 26 (1970), 487-490.
• [2] T. Jech, The Axiom of Choice, North-Holland, Amsterdam, 1973.
• [3] A. Levy, The independence of various definitions of finiteness, Fund. Math. 46 (1958), 1-13.
• [4] D. Pincus, Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods, J. Symbolic Logic 37 (1972), 721-743.
• [5] J. G. Rosenstein, Linear Orderings, Academic Press, New York, 1982.
• [6] G. Sageev, An independence result concerning the axiom of choice, Ann. Math. Logic 8 (1975), 1-184.
• [7] A. Tarski, Sur les ensembles finis, Fund. Math. 6 (1924), 45-95.