03522nam a22005057a 4500
sulb-eb0022359
BD-SySUS
20160413122248.0
cr nn 008mamaa
130125s2013 xxu| s |||| 0|eng d
9781461457466
978-1-4614-5746-6
10.1007/978-1-4614-5746-6
doi
QA8.9-10.3
PBC
bicssc
PBCD
bicssc
MAT018000
bisacsh
511.3
23
Srivastava, Shashi Mohan.
author.
A Course on Mathematical Logic
[electronic resource] /
by Shashi Mohan Srivastava.
2nd ed. 2013.
New York, NY :
Springer New York :
Imprint: Springer,
2013.
XII, 198 p.
online resource.
text
txt
rdacontent
computer
c
rdamedia
online resource
cr
rdacarrier
text file
PDF
rda
Universitext,
0172-5939
Preface -- 1 Syntax of First-Order Logic -- 2 Semantics of First-Order Languages -- 3 Propositional Logic -- 4 Completeness Theorem for First-Order Logic -- 5 Model Theory -- 6 Recursive Functions and Arithmetization of Theories -- 7 Incompleteness Theorems and Recursion Theory -- References -- Index.
This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more. Review from the first edition: "All results included in the book are very carefully selected and proved. The author’s manner of writing is excellent, which will surely make this book useful to many categories of readers." --Marius Tarnauceanu, Zentralblatt MATH.
Mathematics.
Mathematical logic.
Algebra.
Mathematics.
Mathematical Logic and Foundations.
Mathematical Logic and Formal Languages.
Algebra.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9781461457459
Universitext,
0172-5939
http://dx.doi.org/10.1007/978-1-4614-5746-6
ZDB-2-SMA
Dewey Decimal Classification
eBooks
44451
44451