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.

/pdf/uniform-central-limit-theorems-2w96qbq58m.pdf

Uniform Central Limit Theorems

A Dual Form of Ramsey's Theorem

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.

/pdf/mathematical-thought-and-its-objects-520cqh4gid.pdf

Mathematical Thought and its Objects

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.

Higher-Order Logic

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.

F. R. Drake

Papers

Set theory : an introduction to large cardinals