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Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics 1st edition by Douglas Cenzer, Jean Larson, Christopher Porter, Jindrich Zapletal ISBN 9811243840 9789811243844

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Degree Set Theory Prof Lalji Prasad Digital Instant Download

Author(s): Prof Lalji Prasad
ISBN(s): 9788193765272, 8193765273
Edition: Revised Edition
File Details: PDF, 253.06 MB
Year: 2018
Language: english
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Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics 1st edition by Douglas Cenzer, Jean Larson, Christopher Porter, Jindrich Zapletal – Ebook PDF Instant Download/Delivery: 9811243840, 978-9811243844
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ISBN 10:    9811243840
ISBN 13: 978-9811243844
Author:        Douglas Cenzer, Jean Larson, Christopher Porter, Jindrich Zapletal

This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Gödel’s Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy.
 

Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics 1st Table of contents:

1. Introduction

2. Propositional Logic

2.1 Basic Definitions
2.2 Truth Interpretations
2.3 The Disjunctive Normal Form Theorem
2.4 The Deductive Calculus
2.5 The Soundness Theorem
2.6 The Completeness Theorem
2.7 Completeness, Consistency, and Independence
2.8 Logical vs. Topological Compactness

3. Predicate Logic

3.1 The Language of Predicate Logic
3.2 Structures
3.3 The Deductive Calculus
3.4 Soundness Theorem for Predicate Logic

4. Models of Predicate Logic

4.1 The Completeness Theorem for Predicate Logic
4.2 Compactness
4.3 Isomorphism and Elementary Equivalence
4.4 Models, Theories, and Axioms
4.5 Categoricity and Quantifier Elimination
4.6 Examples of Theories and Structures

5. Boolean Algebras

5.1 Properties and Examples of Boolean Algebras
5.2 The Partial Ordering on a Boolean Algebra
5.3 Filters and Ideals
5.4 Ultraproducts

6. Computability

6.1 Finite State Machines
6.2 Turing Machines
6.3 Recursive Functions
6.4 The Halting Problem

7. Decidable and Undecidable Theories

7.1 Decidable vs. Undecidable Logical Systems
7.2 Decidable Theories
7.3 Gödel’s Incompleteness Theorems

8. Algorithmic Randomness

8.1 Kolmogorov Complexity
8.2 Incompressible Strings
8.3 Kolmogorov Complexity and Incompleteness

9. Nonstandard Numbers

9.1 Nonstandard Natural Numbers
9.2 Nonstandard Analysis

10. Foundations of Geometry

10.1 Axioms of Plane Geometry
10.2 Non-Euclidean Models
10.3 Finite Geometries

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