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Total Size:
1.6 MB
Info Hash:
7183FAD43D414AD9A4C0E3DDF2AE925E04BC5506
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Added:
Aug. 6, 2025, 10:02 a.m.
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(Last updated: Aug. 6, 2025, 10:03 a.m.)
| File | Size |
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| Buss S. Introduction to Mathematical Logic 2023.pdf | 1.6 MB |
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11.4 MB
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2025-05-18
| Uploaded by andryold1 | Size 11.4 MB | Health [ 21 /17 ] | Added 2025-05-18 |
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SOURCE: Buss S. Introduction to Mathematical Logic 2023
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COVER
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MEDIAINFO
Textbook in PDF format This book provides an introduction to propositional and first logic with an emphasis on mathematical development and rigorous proofs. The first chapters (Chapters I-IV) cover the completeness and soundness theorems for propositional and first-order logic. The next three chapters cover algorithms and Turing machines, and finally the Gödel Second Incompleteness Theorem. A final still-to-be-written Chapter ? covers Herbrand’s Theorem as an optional topic. An appendix—also still-to-be written—covers primitive recursive and partial recursive functions. The book is intended as an undergraduate textbook in mathematical logic, intended chiefly for students in mathematics, computer science and philosophy. The reader is expected to have a certain level of mathematical sophistication, especially the willingness to deal with abstraction and mathematical proofs. However, the book does not presuppose much in the way of prerequisites or mathematical knowledge. Apart from some short sections that discuss algebraic structures (such as groups and fields), most of the mathematical prerequisites will be covered in a course in discrete mathematics. In addition, it is expected that readers will be comfortable with reading and writing (informal) mathematical proofs. My goal in writing this book was to write an elementary and straightforward introduction to classical logic, which is still mathematically rigorous. The proof systems used in the book are conventional proof systems (called “PL” and “FO”) with modus ponens and generalization as the main inference rules. Other proof systems are certainly possible, but PL and FO are arguably the most straightforward and most traditional proof systems. Considerable efforts have been made to streamline the presentation without skimping unduly on mathematical rigor. Only countable languages are covered, but uncountable languages are treated in a few of the exercises
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