Consequences of the axiom of choice / Paul Howard, Jean E. RubinType de document : MonographieCollection : Mathematical surveys and monographs, 59Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1998Description : 1 vol. (VII-432 p.) ; 26 cmISBN : 9780821809778.ISSN : 0885-4653.Bibliographie : Bibliogr. pp. 389-419. Index.Sujet MSC : 03-00, General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations
03E25, Mathematical logic and foundations - Set theory, Axiom of choice and related propositions
03-02, Research exposition (monographs, survey articles) pertaining to mathematical logic and foundationsEn-ligne : Zentralblatt | MathSciNet | AMS
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disquette inclus dans livre
Bibliogr. pp. 389-419. Index
This book, Consequences of the Axiom of Choice, is a comprehensive listing of statements that have been proved in the last 100 years using the axiom of choice. Each consequence, also referred to as a form of the axiom of choice, is assigned a number.
Part I is a listing of the forms by number. In this part each form is given together with a listing of all statements known to be equivalent to it (equivalent in set theory without the axiom of choice). In Part II the forms are arranged by topic. In Part III we describe the models of set theory which are used to show non-implications between forms. Part IV, the notes section, contains definitions, summaries of important sub-areas and proofs that are not readily available elsewhere. Part V gives references for the relationships between forms and Part VI is the bibliography.
Part VII is contained on the floppy disk which is enclosed in the book. It contains a table with form numbers as row and column headings. The entry in the table in row n, column k gives the status of the implication "form n implies form k". Software for easily extracting information from the table is also provided. (source : AMS)