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Model Theory by
Call Number: ONLINE and 12 Ch
Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory.
Mathematical Logic by
Call Number: 12 Sh
This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject.
A Course in Model Theory by
Call Number: ONLINE
Publication Date: 2012-05-07
This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.
Set Theory by
Call Number: 13 Je
This monograph covers the recent major advances in various areas of set theory. From the reviews: "One of the classical textbooks and reference books in set theory....The present 'Third Millennium' edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS
Basic Set Theory by
Call Number: 13 Le 2002
Publication Date: 2002-08-13
Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
מיון הנושאים 10-18
10 Logic and Foundations
11 Traditional logic. Modal logic. Temporal logic. Dynamical and other logics
12 Mathematical logic. Symbolic logic. Semantics. Model theory. Nonstandard analysis
13 Set theory. Foundations of arithmetics. Algebra and analysis
14 Metamathematics. Proof theory. Axiomatics
15 Philosophy of mathematics. Philosophy of sciences. Foundations of mathematics
16 Computable functions (Recursive function theory). Recursive arithmetics. Computability. Recursion theory
17 Decision problems
18 Automata (see also 252.2) Mathematical machines and languages. Artificial intelligence (see also 236).
See also: Computer Science - Subject Classification System