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Model theorythe algebraic basics /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Model theoryby Davide Rizza.
其他題名:	the algebraic basics /
作者:	Rizza, Davide.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xxiii, 524 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Model theory.
電子資源:	https://doi.org/10.1007/978-3-032-03796-1
ISBN:	9783032037961$q(electronic bk.)

Model theorythe algebraic basics /
Rizza, Davide.

Model theorythe algebraic basics /[electronic resource] :by Davide Rizza. - Cham :Springer Nature Switzerland :2025. - xxiii, 524 p. :ill., digital ;24 cm. - Trends in logic, studia logica library,v. 702212-7313 ;. - Trends in logic, studia logica library ;v.41..

1 Some concrete structures -- 2 Languages and Structures -- 3 Theories and models -- 4 Morphisms, substructures and extensions -- 5 Ultraproducts -- 6 Essential field theory -- 7 Complete theories -- 8 Model-completeness and quantifier elimination -- 9 Types -- 10 Algebraically closed fields and algebraic geometry -- 11 Real closed fields -- 12 Fraisse limits and measurement scales -- Further Reading -- Appendix A. Set-theoretic background -- Appendix B. Solutions to Exercises -- Bibliography -- Index.

This textbook is a gently-paced, comprehensive introduction to model theory suitable for students of philosophy, linguistics, computer science, or mathematics who specialise in logic. The book assumes no preliminary knowledge of logic or algebra beyond the barest rudiments of set theory. After a thorough discussion of the elements of model theory (languages, structures, morphisms), the reader is led into a study of key model-theoretic properties (quantifier elimination, model-completeness), ideas (types, Morley rank) and classic applications (to groups, vector spaces, algebraically closed and real closed fields). The book also discusses applications of model-theoretic ideas to philosophy and mathematical social science. More than 300 exercises with full solutions are designed to consolidate understanding and build confidence. A set-theoretic appendix covers in detail the theory of ordinal and cardinal numbers needed in the second half of the book.

ISBN: 9783032037961$q(electronic bk.)

Standard No.: 10.1007/978-3-032-03796-1doiSubjects--Topical Terms:

191661
Model theory.

LC Class. No.: QA9.7

Dewey Class. No.: 511.34

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505 0 $a 1 Some concrete structures -- 2 Languages and Structures -- 3 Theories and models -- 4 Morphisms, substructures and extensions -- 5 Ultraproducts -- 6 Essential field theory -- 7 Complete theories -- 8 Model-completeness and quantifier elimination -- 9 Types -- 10 Algebraically closed fields and algebraic geometry -- 11 Real closed fields -- 12 Fraisse limits and measurement scales -- Further Reading -- Appendix A. Set-theoretic background -- Appendix B. Solutions to Exercises -- Bibliography -- Index.
520 $a This textbook is a gently-paced, comprehensive introduction to model theory suitable for students of philosophy, linguistics, computer science, or mathematics who specialise in logic. The book assumes no preliminary knowledge of logic or algebra beyond the barest rudiments of set theory. After a thorough discussion of the elements of model theory (languages, structures, morphisms), the reader is led into a study of key model-theoretic properties (quantifier elimination, model-completeness), ideas (types, Morley rank) and classic applications (to groups, vector spaces, algebraically closed and real closed fields). The book also discusses applications of model-theoretic ideas to philosophy and mathematical social science. More than 300 exercises with full solutions are designed to consolidate understanding and build confidence. A set-theoretic appendix covers in detail the theory of ordinal and cardinal numbers needed in the second half of the book.
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