Introduction to Mathematical Logics

By 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

• Language: English
• Publisher: BookRix
• Release date: Apr 19, 2023
• ISBN: 9783755439400

Simone Malacrida

Simone Malacrida (1977) Ha lavorato nel settore della ricerca (ottica e nanotecnologie) e, in seguito, in quello industriale-impiantistico, in particolare nel Power, nell'Oil&Gas e nelle infrastrutture. E' interessato a problematiche finanziarie ed energetiche. Ha pubblicato un primo ciclo di 21 libri principali (10 divulgativi e didattici e 11 romanzi) + 91 manuali didattici derivati. Un secondo ciclo, sempre di 21 libri, è in corso di elaborazione e sviluppo.

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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.

I

BASIC MATHEMATICAL LOGIC

BASIC MATHEMATICAL LOGIC

Introduction

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Mathematical logic deals with the coding, in mathematical terms, of intuitive concepts related to human reasoning.

It is the starting point for any mathematical learning process and, therefore, it makes complete sense to expose the elementary rules of this logic at the beginning of the whole discourse.

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We define an axiom as a statement assumed to be true because it is considered self-evident or because it is the starting point of a theory.

Logical axioms are satisfied by any logical structure and are divided into tautologies (true statements by definition devoid of new informative value) or axioms considered true regardless, unable to demonstrate their universal validity.

Non-logical axioms are never tautologies and are called postulates .

Both axioms and postulates are unprovable.

Generally, the axioms