# lectures in logic and set theory volume 2 set theory cambridge studies in advanced mathematics

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## Lectures In Logic And Set Theory Volume 2 Set Theory

**Author :**George Tourlakis

**ISBN :**113943943X

**Genre :**Mathematics

**File Size :**86. 16 MB

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This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.

## Cambridge Studies In Advanced Mathematics

**Author :**George J. Tourlakis

**ISBN :**0521753740

**Genre :**Logic, Symbolic and mathematical

**File Size :**21. 7 MB

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## Lectures In Logic And Set Theory Volume 1 Mathematical Logic

**Author :**George Tourlakis

**ISBN :**1139439421

**Genre :**Mathematics

**File Size :**34. 28 MB

**Format :**PDF

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This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.

## Fundamentals Of Set And Number Theory

**Author :**Valeriy K. Zakharov

**ISBN :**9783110550948

**Genre :**Mathematics

**File Size :**83. 95 MB

**Format :**PDF, ePub, Mobi

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This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language

## Fundamentals Of Functions And Measure Theory

**Author :**Valeriy K. Zakharov

**ISBN :**9783110550962

**Genre :**Mathematics

**File Size :**61. 22 MB

**Format :**PDF, Kindle

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This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals

## Mathematical Reviews

**Author :**

**ISBN :**UVA:X006195256

**Genre :**Mathematics

**File Size :**77. 78 MB

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## Principia Mathematica

**Author :**Alfred North Whitehead

**ISBN :**STANFORD:36105039675058

**Genre :**Logic, Symbolic and mathematical

**File Size :**70. 93 MB

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**Download :**181

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## Introduction To Foliations And Lie Groupoids

**Author :**I. Moerdijk

**ISBN :**1139438980

**Genre :**Mathematics

**File Size :**63. 67 MB

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This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.

## The Core Model Iterability Problem

**Author :**John R. Steel

**ISBN :**9781107167964

**Genre :**Mathematics

**File Size :**66. 98 MB

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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Large cardinal hypotheses play a central role in modern set theory. One important way to understand such hypotheses is to construct concrete, minimal universes, or 'core models', satisfying them. Since Gödel's pioneering work on the universe of constructible sets, several larger core models satisfying stronger hypotheses have been constructed, and these have proved quite useful. In this volume, the eighth publication in the Lecture Notes in Logic series, Steel extends this theory so that it can produce core models having Woodin cardinals, a large cardinal hypothesis that is the focus of much current research. The book is intended for advanced graduate students and researchers in set theory.

## Books In Print

**Author :**R.R. Bowker Company

**ISBN :**UOM:39015054035236

**Genre :**American literature

**File Size :**70. 49 MB

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