Author
F. R. Drake
Bio: F. R. Drake is an academic researcher. The author has contributed to research in topics: Universal set & New Foundations. The author has an hindex of 1, co-authored 1 publications receiving 216 citations.
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219 citations
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Book•
01 Jan 1999TL;DR: In this paper, Donsker's theorem, metric entropy and inequalities, and the universal and uniform central limit theorems are discussed. But they do not consider the two-sample case, the bootstrap case, and confidence sets.
Abstract: Preface 1. Introduction: Donsker's theorem, metric entropy and inequalities 2. Gaussian measures and processes sample continuity 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis and related classes 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance principles 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems Appendices Subject index Author index Index of notation.
697 citations
TL;DR: The dual form of the Ramsey's Theorem with colorings of the k-element subsets of ω was shown in this paper, where the coloring of the partitions of the subsets was replaced by the color of the blocks.
148 citations
Book•
12 Nov 2009TL;DR: In this article, a problem about sets is formulated as a set-theoretic problem about logic and modality and structuralism, and the problem is solved by reasoning about sets.
Abstract: Preface 1. Objects and logic 2. Structuralism and nominalism 3. Modality and structuralism 4. A problem about sets 5. Intuition 6. Numbers as objects 7. Intuitive arithmetic and its limits 8. Mathematical induction 9. Reason.
141 citations
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TL;DR: First-order logic was a modest fragment of the more ambitious language employed in the logicist program of Frege and Russell as discussed by the authors, which became a stable base for logical theory by 1930, when its interesting and fruitful meta-properties had become clear, such as completeness, compactness and Lowenheim-Skolem.
Abstract: What is nowadays the central part of any introduction to logic, and indeed to some the logical theory par excellence, used to be a modest fragment of the more ambitious language employed in the logicist program of Frege and Russell. ‘Elementary’ or ‘first-order’, or ‘predicate logic’ only became a recognized stable base for logical theory by 1930, when its interesting and fruitful meta-properties had become clear, such as completeness, compactness and Lowenheim-Skolem. Richer higher-order and type theories receded into the background, to such an extent that the (re-) discovery of useful and interesting extensions and variations upon first-order logic came as a surprise to many logicians in the sixties.
120 citations
TL;DR: In this article, G. Boolos proposed a scheme distinguant les quantificateurs monadiques and polyadiques, a scheme developpée par G.Boolos.
Abstract: Etude de la critique du consensus entre semantique du premier ordre, semantique du second ordre et theorie des ensembles chez Quine, developpee par G. Boolos a partir d'un scheme distinguant les quantificateurs monadiques et les quantificateurs polyadiques.
115 citations