Equivalents of the Axiom of Choice, IIElsevier, 1 mars 1985 - 321 pages This monograph contains a selection of over 250 propositions which are equivalent to AC. The first part on set forms has sections on the well-ordering theorem, variants of AC, the law of the trichotomy, maximal principles, statements related to the axiom of foundation, forms from algebra, cardinal number theory, and a final section of forms from topology, analysis and logic. The second part deals with the axiom of choice for classes - well-ordering theorem, choice and maximal principles. |
Table des matières
| 1 | |
Class Forms | 185 |
List of the Set Forms | 247 |
List of the Class Forms | 271 |
List of Forms Related to the Axiom of Choice | 279 |
Bibliography | 289 |
Index of Authors | 305 |
Index of Symbols | 311 |
Index of Technical Terms | 315 |
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Expressions et termes fréquents
abelian group aleph AS&C axiom of choice axiom of foundation bijection Boolean algebra c-maximal subclass c-maximal subset choice function class form contains a C-maximal contradiction Define a function Define a relation definition disjoint sets equivalent exists a c-maximal exists a natural f-chain Felgner finite character function f implies the axiom infinite sets lattice Let f linear linearly ordered mapping maximal principle natural number nest non-empty class non-empty sets normed vector space ordinal number pairwise disjoint partial ordering partial ordering relation PROOF proper class proper ideal property of finite prove Q-ordered R-maximal element R-upper bound Rubin satisfy the hypothesis set form set of non-empty Sierpinski Sobocinski subalgebra subspace Suppose Tarski topology TR&C transfinite u e x vector space well-ordering theorem