Mathematical Logic Propositional Calculus Boolean Algebras Predicate Calculus

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Mathematical Logic Part 1
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Author : René Cori
language : en
Publisher: OUP Oxford
Release Date : 2000-09-07
Mathematical Logic Part 1 written by René Cori and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-07 with Mathematics categories.
Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. In particular, it is a major element in theoretical computer science and has undergone a huge revival with the explosion of interest in computers and computer science. This book provides students with a clear and accessible introduction to this important subject. The concept of model underlies the whole book, giving the text a theoretical coherence whilst still covering a wide area of logic.
Mathematical Logic
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Author : René Cori
language : en
Publisher: OUP Oxford
Release Date : 2000
Mathematical Logic written by René Cori and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. It is a major element in theoretical computer science and has undergone a huge revival with the every- growing importance of computer science. This text is based on a course to undergraduates and provides a clear and accessible introduction to mathematical logic. The concept of model provides the underlying theme, giving the text a theoretical coherence whilst still covering a wide area of logic. The foundations having been laid in Part I, this book starts with recursion theory, a topic essential for the complete scientist. Then follows Godel's incompleteness theorems and axiomatic set theory. Chapter 8 provides an introduction to model theory. There are examples throughout each section, and varied selection of exercises at the end. Answers to the exercises are given in the appendix.
Mathematical Logic Propositional Calculus Boolean Algebras Predicate Calculus
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Author : René Cori
language : en
Publisher: Oxford University Press on Demand
Release Date : 2000
Mathematical Logic Propositional Calculus Boolean Algebras Predicate Calculus written by René Cori and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students will study. Assuming no prior knowledge of the topic, this book provides an accessible introduction for advanced undergraduate students.
Mathematical Logic Propositional Calculus Boolean Algebras Predicate Calculus Pt 2 Recursion Theory G Del S Theorems Set Theory Model Theory
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Author : René Cori
language : en
Publisher:
Release Date : 2000
Mathematical Logic Propositional Calculus Boolean Algebras Predicate Calculus Pt 2 Recursion Theory G Del S Theorems Set Theory Model Theory written by René Cori and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Logic, Symbolic and mathematical categories.
Boolean Reasoning
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Author : Frank Markham Brown
language : en
Publisher: Courier Corporation
Release Date : 2012-02-10
Boolean Reasoning written by Frank Markham Brown and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-10 with Mathematics categories.
Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.
Boolean Algebras
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Author : Roman Sikorski
language : en
Publisher: Springer
Release Date : 2013-11-11
Boolean Algebras written by Roman Sikorski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [IJ. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know ledge of latticetheory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs.
Introduction To Mathematical Logic
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Author : Elliot Mendelsohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Mathematical Logic written by Elliot Mendelsohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.
Algebraic Methods Of Mathematical Logic
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Author : Ladislav Rieger
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Algebraic Methods Of Mathematical Logic written by Ladislav Rieger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-mathematical parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semantic rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.
A Course In Mathematical Logic For Mathematicians
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Author : Yu. I. Manin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-13
A Course In Mathematical Logic For Mathematicians written by Yu. I. Manin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-13 with Mathematics categories.
1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.
History Of Mathematical Logic From Leibniz To Peano
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Author :
language : en
Publisher:
Release Date : 1969
History Of Mathematical Logic From Leibniz To Peano written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.