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Combinatorial Set Theory
This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.
Combinatorial Set Theory
This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of se...
Gödel's Theorems and Zermelo's Axioms
This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
Fast Track to Forcing
For those who wonder if the forcing theory is beyond their means: no. Directions to research in forcing are given.
Over getallen gesproken - Talking about numbers
Wilt u iets weten over getallen? De auteur neemt u in deze 4de, herziene druk mee op de voortzetting van zijn persoonlijke ontdekkingsreis in de getaltheorie. 757 getallenverzamelingen geven een indrukwekkend beeld van getallen die voor veel mensen onbekend zijn. Veel worden er dagelijks gebruikt en toegepast zonder dat we ons dat bewust zijn. Ze spelen een rol in wetenschap en samenleving. Een intensieve ontdekkingsreis heeft ze ontsloten, in alfabetische volgorde geplaatst, verklaard en voorzien van interessante toevoegingen. Apart wordt aandacht besteed aan getallen met verrassende eigenschappen en aan Bijbelse getallen met wiskundige relaties. Om het boek voor een breed publiek toegankel...
Das Schweizer Buch
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The Axiom of Choice
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Statistical Methods for Modeling Human Dynamics
This interdisciplinary volume features contributions from researchers in the fields of psychology, neuroscience, statistics, computer science, and physics. State-of-the-art techniques and applications used to analyze data obtained from studies in cognition, emotion, and electrophysiology are reviewed along with techniques for modeling in real time and for examining lifespan cognitive changes, for conceptualizing change using item response, nonparametric and hierarchical models, and control theory-inspired techniques for deriving diagnoses in medical and psychotherapeutic settings. The syntax for running the analyses presented in the book is provided on the Psychology Press site. Most of the ...
