Independence results for class forms of the axiom of choice
Journal of Symbolic Logic 43 (4):673-684 (1978)
| Abstract | Let NBG be von Neumann-Bernays-Gödel set theory without the axiom of choice and let NBGA be the modification which allows atoms. In this paper we consider some of the well-known class or global forms of the wellordering theorem, the axiom of choice, and maximal principles which are known to be equivalent in NBG and show they are not equivalent in NBGA | |||||||||
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Mitchell Spector (1988). Ultrapowers Without the Axiom of Choice. Journal of Symbolic Logic 53 (4):1208-1219.
Vivian Charles Walsh (1967). On the Significance of Choice Sets with Incompatibilities. Philosophy of Science 34 (3):243-250.
Omar De La Cruz, Eric Hall, Paul Howard, Jean E. Rubin & Adrienne Stanley (2002). Definitions of Compactness and the Axiom of Choice. Journal of Symbolic Logic 67 (1):143 - 161.
David W. Miller (2007). Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice. Logica Universalis 1 (1).
Andrea Cantini (2003). The Axiom of Choice and Combinatory Logic. Journal of Symbolic Logic 68 (4):1091-1108.
Lorenz Halbeisen & Saharon Shelah (2001). Relations Between Some Cardinals in the Absence of the Axiom of Choice. Bulletin of Symbolic Logic 7 (2):237-261.
Paul E. Howard (1973). Limitations on the Fraenkel-Mostowski Method of Independence Proofs. Journal of Symbolic Logic 38 (3):416-422.
Paul Howard & Jean E. Rubin (1995). The Axiom of Choice for Well-Ordered Families and for Families of Well- Orderable Sets. Journal of Symbolic Logic 60 (4):1115-1117.
G. P. Monro (1983). On Generic Extensions Without the Axiom of Choice. Journal of Symbolic Logic 48 (1):39-52.
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