Introduction to Mathematical Logics E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

In this book, all facets of mathematical logic are presented such as: symbology, principles and properties of elementary logic boolean logic order theory and axiomatic systems axiomatic set theory and Godel's theorems logical paradoxes and logical antinomies descriptive and fuzzy logics number theory and modular arithmetic

Leseprobe

Simone Malacrida

Introduction to Mathematical Logics

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

"Introduction to Mathematical Logics"

INTRODUCTION

BASIC MATHEMATICAL LOGIC

ADVANCED MATHEMATICAL LOGIC

NUMBER THEORY

"Introduction to Mathematical Logics"

"Introduction to Mathematical Logics"

SIMONE MALACRIDA

In this book, all facets of mathematical logic are presented such as:

symbology, principles and properties of elementary logic

boolean logic

order theory and axiomatic systems

axiomatic set theory and Godel's theorems

logical paradoxes and logical antinomies

descriptive and fuzzy logics

number theory and modular arithmetic

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Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – BASIC MATHEMATICAL LOGIC

Introduction

Symbology

Principles

Property

Boolean logic

Applications of logic: proof of theorems

Applications of Boolean logic: electronic calculators

Insight: syllogism and mathematical logic

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II – ADVANCED MATHEMATICAL LOGIC

Order theory

Robinson and Peano arithmetic

Axiomatic systems

Axiomatic set theory

Godel's theorems

Paradoxes and antinomies

Other logical systems

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III – NUMBER THEORY

Definitions

Modular arithmetic

INTRODUCTION

INTRODUCTION

This book presents all the topics concerning mathematical logic which is the basic tool for understanding any subsequent scientific knowledge.

First, basic knowledge is introduced, such as the use of logical connectors, logical definitions and terminology, as well as Boolean logic and logical principles already used by the ancients.

Subsequently, the purely modern and contemporary part of logic will be exposed, such as the theory of orders and the axiomatic theory of sets, giving ample space to axiomatic systems and the fundamental theorems of Godel, one of the cornerstones of twentieth-century knowledge.

Logical paradoxes and antinomies are a prerequisite for overcoming normal mathematical logic, towards much more open schemes, such as that of fuzzy logic.

Finally, number theory and modular arithmetic are a testing ground for logic itself, still having to prove many conjectures.

The cut of the book is deliberately technical and concise, just to get lost in frills and to give the reader a clear picture of a discipline halfway between mathematics and philosophy.

The first chapter can be understood through high school knowledge, while the next two certainly require university notions.

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