| 书目名称 | Handbook of Set Theory | | 编辑 | Matthew Foreman,Akihiro Kanamori | | 视频video | | | 概述 | Definitive compendium of all of modern set theory.Chapters written by the leading experts in their areas.Carefully crafted, self-contained expositions for all the subfields of set theory.No other up-t | | 图书封面 |  | | 描述 | Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships | | 出版日期 | Book 2010 | | 关键词 | Arithmetic; Combinatorics; Continuum; Determinacy; Equivalence; Large Cardinals; Lemma; cardinals; set theor | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4020-5764-9 | | isbn_softcover | 978-94-024-0466-1 | | isbn_ebook | 978-1-4020-5764-9 | | copyright | Springer Science+Business Media B.V. 2010 |
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发表于 2025-3-21 17:42:10
