Classical Mathematical Logic : : The Semantic Foundations of Logic / / Richard L. Epstein.
In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2011] ©2006 |
Year of Publication: | 2011 |
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Epstein, Richard L., author. aut http://id.loc.gov/vocabulary/relators/aut Classical Mathematical Logic : The Semantic Foundations of Logic / Richard L. Epstein. Course Book Princeton, NJ : Princeton University Press, [2011] ©2006 1 online resource (544 p.) : 20 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Contents -- Preface -- Acknowledgments -- Introduction -- I. Classical Propositional Logic -- II. Abstracting and Axiomatizing Classical Propositional Logic -- III. The Language of Predicate Logic -- IV. The Semantics of Classical Predicate Logic -- V. Substitutions and Equivalences -- VI. Equality -- VII. Examples of Formalization -- VIII. Functions -- IX. The Abstraction of Models -- X. Axiomatizing Classical Predicate Logic -- XI. The Number of Objects in the Universe of a Model -- XII. Formalizing Group Theory -- XIII. Linear Orderings -- XIV. Second-Order Classical Predicate Logic -- XV. The Natural Numbers -- XVI. The Integers and Rationals -- XVII. The Real Numbers -- XVIII. One-Dimensional Geometry -- XIX. Two-Dimensional Euclidean Geometry -- XX. Translations within Classical Predicate Logic -- XXI. Classical Predicate Logic with Non-Referring Names -- XXII. The Liar Paradox -- XXIII. On Mathematical Logic and Mathematics -- Appendix: The Completeness of Classical Predicate Logic Proved by Gödel's Method -- Summary of Formal Systems -- Bibliography -- Index of Notation -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Logic, Symbolic and mathematical. Semantics (Philosophy). MATHEMATICS / Logic. bisacsh Szczerba, Leslaw W. Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691123004 https://doi.org/10.1515/9781400841554 https://www.degruyter.com/isbn/9781400841554 Cover https://www.degruyter.com/cover/covers/9781400841554.jpg |
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English |
format |
eBook |
author |
Epstein, Richard L., Epstein, Richard L., |
spellingShingle |
Epstein, Richard L., Epstein, Richard L., Classical Mathematical Logic : The Semantic Foundations of Logic / Frontmatter -- Contents -- Preface -- Acknowledgments -- Introduction -- I. Classical Propositional Logic -- II. Abstracting and Axiomatizing Classical Propositional Logic -- III. The Language of Predicate Logic -- IV. The Semantics of Classical Predicate Logic -- V. Substitutions and Equivalences -- VI. Equality -- VII. Examples of Formalization -- VIII. Functions -- IX. The Abstraction of Models -- X. Axiomatizing Classical Predicate Logic -- XI. The Number of Objects in the Universe of a Model -- XII. Formalizing Group Theory -- XIII. Linear Orderings -- XIV. Second-Order Classical Predicate Logic -- XV. The Natural Numbers -- XVI. The Integers and Rationals -- XVII. The Real Numbers -- XVIII. One-Dimensional Geometry -- XIX. Two-Dimensional Euclidean Geometry -- XX. Translations within Classical Predicate Logic -- XXI. Classical Predicate Logic with Non-Referring Names -- XXII. The Liar Paradox -- XXIII. On Mathematical Logic and Mathematics -- Appendix: The Completeness of Classical Predicate Logic Proved by Gödel's Method -- Summary of Formal Systems -- Bibliography -- Index of Notation -- Index |
author_facet |
Epstein, Richard L., Epstein, Richard L., Szczerba, Leslaw W. |
author_variant |
r l e rl rle r l e rl rle |
author_role |
VerfasserIn VerfasserIn |
author2 |
Szczerba, Leslaw W. |
author2_variant |
l w s lw lws |
author2_role |
TeilnehmendeR |
author_sort |
Epstein, Richard L., |
title |
Classical Mathematical Logic : The Semantic Foundations of Logic / |
title_sub |
The Semantic Foundations of Logic / |
title_full |
Classical Mathematical Logic : The Semantic Foundations of Logic / Richard L. Epstein. |
title_fullStr |
Classical Mathematical Logic : The Semantic Foundations of Logic / Richard L. Epstein. |
title_full_unstemmed |
Classical Mathematical Logic : The Semantic Foundations of Logic / Richard L. Epstein. |
title_auth |
Classical Mathematical Logic : The Semantic Foundations of Logic / |
title_alt |
Frontmatter -- Contents -- Preface -- Acknowledgments -- Introduction -- I. Classical Propositional Logic -- II. Abstracting and Axiomatizing Classical Propositional Logic -- III. The Language of Predicate Logic -- IV. The Semantics of Classical Predicate Logic -- V. Substitutions and Equivalences -- VI. Equality -- VII. Examples of Formalization -- VIII. Functions -- IX. The Abstraction of Models -- X. Axiomatizing Classical Predicate Logic -- XI. The Number of Objects in the Universe of a Model -- XII. Formalizing Group Theory -- XIII. Linear Orderings -- XIV. Second-Order Classical Predicate Logic -- XV. The Natural Numbers -- XVI. The Integers and Rationals -- XVII. The Real Numbers -- XVIII. One-Dimensional Geometry -- XIX. Two-Dimensional Euclidean Geometry -- XX. Translations within Classical Predicate Logic -- XXI. Classical Predicate Logic with Non-Referring Names -- XXII. The Liar Paradox -- XXIII. On Mathematical Logic and Mathematics -- Appendix: The Completeness of Classical Predicate Logic Proved by Gödel's Method -- Summary of Formal Systems -- Bibliography -- Index of Notation -- Index |
title_new |
Classical Mathematical Logic : |
title_sort |
classical mathematical logic : the semantic foundations of logic / |
publisher |
Princeton University Press, |
publishDate |
2011 |
physical |
1 online resource (544 p.) : 20 line illus. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Acknowledgments -- Introduction -- I. Classical Propositional Logic -- II. Abstracting and Axiomatizing Classical Propositional Logic -- III. The Language of Predicate Logic -- IV. The Semantics of Classical Predicate Logic -- V. Substitutions and Equivalences -- VI. Equality -- VII. Examples of Formalization -- VIII. Functions -- IX. The Abstraction of Models -- X. Axiomatizing Classical Predicate Logic -- XI. The Number of Objects in the Universe of a Model -- XII. Formalizing Group Theory -- XIII. Linear Orderings -- XIV. Second-Order Classical Predicate Logic -- XV. The Natural Numbers -- XVI. The Integers and Rationals -- XVII. The Real Numbers -- XVIII. One-Dimensional Geometry -- XIX. Two-Dimensional Euclidean Geometry -- XX. Translations within Classical Predicate Logic -- XXI. Classical Predicate Logic with Non-Referring Names -- XXII. The Liar Paradox -- XXIII. On Mathematical Logic and Mathematics -- Appendix: The Completeness of Classical Predicate Logic Proved by Gödel's Method -- Summary of Formal Systems -- Bibliography -- Index of Notation -- Index |
isbn |
9781400841554 9783110442502 9780691123004 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA9 |
callnumber-sort |
QA 19 E67 42011EB |
url |
https://doi.org/10.1515/9781400841554 https://www.degruyter.com/isbn/9781400841554 https://www.degruyter.com/cover/covers/9781400841554.jpg |
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Illustrated |
doi_str_mv |
10.1515/9781400841554 |
oclc_num |
979582764 |
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Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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Classical Mathematical Logic : The Semantic Foundations of Logic / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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