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Mathematical Logic

Author: H -D Ebbinghaus; J Flum; W Thomas
Publisher: New York, NY : Springer New York, 1994.
Series: Undergraduate texts in mathematics.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Summary:
This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: H -D Ebbinghaus; J Flum; W Thomas
ISBN: 9781475723557 1475723555
OCLC Number: 851760204
Language Note: English.
Description: 1 online resource (x, 290 pages)
Contents: A --
I Introduction --
II Syntax of First-Order Languages --
III Semantics of First-Order Languages --
IV A Sequent Calculus --
V The Completeness Theorem --
VI The Löwenheim-Skolem and the Compactness Theorem --
VII The Scope of First-Order Logic --
VIII Syntactic Interpretations and Normal Forms --
B --
IX Extensions of First-Order Logic --
X Limitations of the Formal Method --
XI Free Models and Logic Programming --
XII An Algebraic Characterization of Elementary Equivalence --
XIII Lindström's Theorems --
References --
Symbol Index.
Series Title: Undergraduate texts in mathematics.
Responsibility: by H.-D. Ebbinghaus, J. Flum, W. Thomas.

Abstract:

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and  Read more...

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"...the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level." - Journal of Symbolic Logic

 
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Thomas<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/viaf.org\/viaf\/54214837<\/a>> ; # J. Flum<\/span>\n\u00A0\u00A0\u00A0\nschema:creator<\/a> <http:\/\/viaf.org\/viaf\/108792446<\/a>> ; # H-D Ebbinghaus<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"1994<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"This junior\/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most striking results are contained in Goedel\'s work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel\'s theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot\'s undecidability theorem. 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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/899983#Series\/undergraduate_texts_in_mathematics<\/a>> # Undergraduate texts in mathematics.<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:PublicationSeries<\/a> ;\u00A0\u00A0\u00A0\nschema:hasPart<\/a> <http:\/\/www.worldcat.org\/oclc\/851760204<\/a>> ; # Mathematical Logic<\/span>\n\u00A0\u00A0\u00A0\nschema:name<\/a> \"Undergraduate texts in mathematics.<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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<http:\/\/viaf.org\/viaf\/108792446<\/a>> # H-D Ebbinghaus<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Ebbinghaus<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"H.-D<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"H-D Ebbinghaus<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/24669221<\/a>> # W. Thomas<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Thomas<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"W.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"W. Thomas<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/54214837<\/a>> # J. Flum<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Flum<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"J.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"J. Flum<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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