Title
Mathematical Logic, 2Nd Edition (Undergraduate Texts In Mathematics)
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What Is A Mathematical Proof? How Can Proofs Be Justified? Are There Limitations To Provability? To What Extent Can Machines Carry Out Mathe Matical Proofs? Only In This Century Has There Been Success In Obtaining Substantial And Satisfactory Answers. The Present Book Contains A Systematic Discussion Of These Results. The Investigations Are Centered Around Firstorder Logic. Our First Goal Is Godel'S Completeness Theorem, Which Shows That The Con Sequence Relation Coincides With Formal Provability: By Means Of A Calcu Lus Consisting Of Simple Formal Inference Rules, One Can Obtain All Conse Quences Of A Given Axiom System (And In Particular, Imitate All Mathemat Ical Proofs). A Short Digression Into Model Theory Will Help Us To Analyze The Expres Sive Power Of The Firstorder Language, And It Will Turn Out That There Are Certain Deficiencies. For Example, The Firstorder Language Does Not Allow The Formulation Of An Adequate Axiom System For Arithmetic Or Analysis. On The Other Hand, This Difficulty Can Be Overcomeeven In The Framework Of Firstorder Logicby Developing Mathematics In Settheoretic Terms. We Explain The Prerequisites From Set Theory Necessary For This Purpose And Then Treat The Subtle Relation Between Logic And Set Theory In A Thorough Manner.
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- Q: What is the focus of 'Mathematical Logic, 2nd Edition'? A: The book primarily focuses on first-order logic, exploring mathematical proofs, their justification, and limitations of provability.
- Q: Who is the author of this book? A: The author of 'Mathematical Logic, 2nd Edition' is H.-D. Ebbinghaus.
- Q: What is the publication date of the book? A: The book was published on June 10, 1994.
- Q: How many pages does the book contain? A: The book contains 301 pages.
- Q: What type of binding does this edition have? A: This edition is available in hardcover binding.
- Q: Is this book suitable for beginners in mathematical logic? A: While the book systematically discusses complex topics, it is generally suited for readers with some foundational knowledge in logic and mathematics.
- Q: Does the book cover model theory? A: Yes, the book includes a short digression into model theory to analyze the expressive power of first-order language.
- Q: What key theorem does the book discuss? A: The book discusses Godel's completeness theorem, which relates consequence relations to formal provability.
- Q: Are there prerequisites for understanding the content? A: Yes, the book explains necessary prerequisites from set theory required to grasp the concepts effectively.
- Q: What edition is this book? A: This is the 2nd edition of 'Mathematical Logic'.