CHAPTER 1 Internal Set Theory Ordinarily in mathematics, when one introduces a new concept one defines it. For example, if this were a book on “blobs” I would begin with a definition of this new predicate: x is a bl

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A General Discrete Velocity Model Including Internal Degrees of Freedom

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• Set theory
• Ordinal numbers
• Proof theory
• Ordinal arithmetic
• Curry–Howard correspondence
• Mathematical logic
• Collision
• Mechanics

Introduction Sometimes it happens in mathematics that, investigating some branch, some area of mathematical objects, we are forced to introduce new kind of objects which were not originally presumed to exist. There is a

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• Logic
• Model theory
• Infinity
• Real closed field
• Ultraproduct
• Zermelo–Fraenkel set theory
• Internal set theory
• Set theory
• Foundations of mathematics
• Mathematics
• Non-standard analysis
• Mathematical logic

CONTENTS 1. Nonstandard analysis on the real line 1. Introduction to nonstandard real line 2. Development of nonstandard analysis 1

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• Abstract algebra
• Ultraproduct
• Internal set
• Set theory
• Real number
• Parametrization
• Zermelo–Fraenkel set theory
• Criticism of non-standard analysis
• Non-standard analysis
• Mathematics
• Mathematical logic

Preface It is a pleasure for me to have the opportunity to write a preface for this book on the foundations of nonstandard analysis by Vladimir Kanovei. It may seem that everything relevant has been said concerning this

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• Philosophy of mathematics
• Infinity
• Z notation
• Zermelo–Fraenkel set theory
• Internal set theory
• Set theory
• Forcing
• Implementation of mathematics in set theory
• Mathematical logic
• Mathematics
• Non-standard analysis