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＜電子ブック＞
Mathematical Logic : An Introduction to Model Theory / by A. Lightstone
(Mathematical Concepts and Methods in Science and Engineering ; 9)

版	1st ed. 1978.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	1978
本文言語	英語
大きさ	XIII, 338 p : online resource
著者標目	*Lightstone, A author SpringerLink (Online service)
件　名	LCSH:Mathematical logic FREE:Mathematical Logic and Foundations
一般注記	I. Statement Systems and Propositional Calculus -- 1. Statement Systems -- 2. Propositional Calculus -- 3. Provable Wffs -- 4. Substitution Theorems -- 5. Duality -- 6. Deducibility and Completeness -- II. Semantical Systems and Predicate Calculus -- 7. Semantical Systems -- 8. Predicate Calculus -- 9. Provable Wffs -- 10. Substitution Theorems -- 11. Duality -- 12. Deducibility and Completeness -- III. Applications -- 13. Nonstandard Analysis -- 14. Normal Semantical Systems -- 15. Axiomatic Set Theory -- 16. Complete Theories -- Symbol Index Before his death in March, 1976, A. H. Lightstone delivered the manu­ script for this book to Plenum Press. Because he died before the editorial work on the manuscript was completed, I agreed (in the fall of 1976) to serve as a surrogate author and to see the project through to completion. I have changed the manuscript as little as possible, altering certain passages to correct oversights. But the alterations are minor; this is Lightstone's book. H. B. Enderton vii Preface This is a treatment of the predicate calculus in a form that serves as a foundation for nonstandard analysis. Classically, the predicates and variables of the predicate calculus are kept distinct, inasmuch as no variable is also a predicate; moreover, each predicate is assigned an order, a unique natural number that indicates the length of each tuple to which the predicate can be prefixed. These restrictions are dropped here, in order to develop a flexible, expressive language capable of exploiting the potential of nonstandard analysis. To assist the reader in grasping the basic ideas of logic, we begin in Part I by presenting the propositional calculus and statement systems. This provides a relatively simple setting in which to grapple with the some­ times foreign ideas of mathematical logic. These ideas are repeated in Part II, where the predicate calculus and semantical systems are studied HTTP:URL=https://doi.org/10.1007/978-1-4615-8750-7

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