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This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.

Set theory --- Logic, Symbolic and mathematical

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Empruntant au Tractatus logico-philosophicus son affirmation d'ouverture - "Le monde est tout ce qui a lieu" - et sa problématique du langage et de la logique, la Grammaire philosophique développe la question de la relation entre le langage et la réalité, dont "l'harmonie, comme tout autre chose métaphysique, est à trouver dans la grammaire du langage" . La Grammaire philosophique concilie les deux orientations de la philosophie de Wittgenstein dans la dynamique de la représentation : le fondement du langage comme celui des mathématiques est convention, et la philosophie, administrant le développement de ces jeux, de ces formes de vie, y apparaît comme la forme suprême de l'imagination. Le concept de grammaire est l'instrument de l'activité philosophique par excellence.

Grammar, Comparative and general --- Logic, symbolic and mathematical --- Inference --- Mathematics

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Pragmatics --- Pragmatics. --- Pragmalinguistics --- General semantics --- Language and languages --- Logic, Symbolic and mathematical --- Semantics (Philosophy) --- Philosophy

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Logic, Symbolic and mathematical. --- Reasoning. --- Lógica simbólica y matemática. --- Razonamiento.

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Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naive and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.

Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics