Mathematical Logic (Oxford Texts in Logic, 3) by Ian Chiswell (PDF)

Description

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can’t be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich’s theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved.Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in logic, mathematics, philosophy, and computer science.

User’s Reviews

Editorial Reviews: About the Author Ian Chiswell acheived a Ph.D. at the University of Michigan in 1973 on the Bass-Serre theory of groups acting on trees. After three years as a temporary lecturer at the University of Birmingham he moved back to Queen Mary, University of London in 1976. His teaching experience dates back to 1968 when he was a teaching fellow at the University of Michigan. He spent the academic year 1972-73 in Germany at the Ruhr-Universitaet Bochum. He has published a monograph on lamda-trees, which are generalisations of ordinary trees. His work has connections with mathematical logic, mainly via non-standard free groups. Wilfrid Hodges achieved his DPhil at Oxford in 1970 for a thesis in model theory (mathematical logic). He has taught mathematics at London University for nearly forty years, first at Bedford College and then at Queen Mary, and also taught for visiting years in Los Angeles and Boulder (USA). Besides this book, he has four other textbooks of logic in print, at levels rangingfrom popular to research. He has served as president of the British Logic Colloquium and the European Association for Logic, Language and Information, and as vice-president of the London Mathematical Society.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐It is very unfair that this book, as of 01/12/2014, has a 3 stars rating. The two sad reviews giving 1 and 3 stars to the book are seriously mistaken. One is complaining because the book “[d]oes not touch on Wittgenstein’s Logic from the Tractatus Logico Philosophicus.”. The other one says that the book “(…) seems like the product of a mathematician who desired to create a textbook without knowing what he was getting himself into but finished it for the sake of finishing it.”. These are just too embarrassing to comment further.If something is to be a reason to detract, say, one star tops, then let it be the price. Indeed, for the sheer material aspect of the book (number of pages, paper quality, etc) it seems there is no good reason for it to cost $62.00 bucks, on the other hand the actual logical material presented in the book is so didactic, nicely presented along snippets about key concepts and logicians, that it worths the price paid twice! No other book can compare to this one in terms of efficiency, being the sole complain that it is too short.Maybe we can hope for another enlarged edition in the future to cover second order logic.This is the ideal book for those who struggled with a Van Dalen or the like.

⭐The book is fundamental in the first chapter but quickly moves on to logic diagrams and parsing trees. Chapter 3 is hard for the beginning student and advanced student because of the multiple clauses. The History of Logic is well thought out in introducing several key figures in the history like Charles Pierce, and David Hilbert. The exercises are difficult so I would have to say have another 2-4 logic references with you, one being Quine’s Methods of Logic. Does not touch on Wittgenstein’s Logic from the Tractatus Logico Philosophicus. There are numerous gaps in the book so this cannot be a comprehensive reference either.

⭐Such an excellent text. I congratulate logician Wilfred Hodges whose works I have had the honour of studying. This is an excellent text in following sense.A deep complex work in mathematical logic would be at least 600+ pages of pure mathematical reasoning. I did a Masters course with the brilliant Moshe Machover (A course in mathematical logic, which he wrote with John Bell).But a rigorous account convering Quantificational Logic, Model Theory, Recursive Functions and large proofs (such as that of Putnam, Davis, Matyasevich’s theorem), Formal Set Theory, Non-standard Analysis, would at lease be as long as Machover’s book — in fact, a long-hand explanation of what he did in the book, solutions of exercises would make the book at least 800 pages.So then, if you don’t have a career in logic and logic-related sciences in mind, you can get a great introduction here to logic by one of recent logic’s icons. His Model Theory book is something of a bible.Once you appetite is whetted for Logic by this book, you might next go to Category Theory/Topos approach to logic in the Lawvere’s expose: conceptual mathematics (2nd Edition!).From then on sky is the limit: You can tend to that limit via the work of Saunders Maclane in SHEAVES in Geometry and Logic. But for the non-mathematician, this book is ENTIRELY inaccessible.A WORD or two of HOPE ! Mathematics is like a large tapestry and one mustn’t be too fussy about the EXACT coverage of “everything” you want in a book. The point is that as you read an good book – -like Hodge’s — you will have learnt a portion of that tapestry. The next book will conver more of it, you can skip the parts you have read from Hodges or Lawvere’s or find them more easily workable.The most difficult part of doing logic/mathematics is ballancing the pace of working and the mind-set for studying it. I read a partial account of how in musical training in 18th century getting the mind to be in the right attitude was the central focus – which was part of the environment of creativity.

⭐Sul libro niente da dire, forse il miglior manuale di introduzione alla logica del primo ordine. Come tutti i libri stampati da amazon la qualità di stampa è pessima, è come se fosse stampato con del toner sul punto di finire. Andrebbe segnalato quando il libro è stampato da amazon dal momento che la cosa significa SEMPRE acquistare un libro stampato male: finche il libro costa poco posso anche accettare la qualità bassa e procedere all’acquisto ma in questo caso si tratta di un volume da 50 euro, quindi ritrovarselo pure sbiadito è irritante.

⭐

Keywords

Free Download Mathematical Logic (Oxford Texts in Logic, 3) in PDF format
Mathematical Logic (Oxford Texts in Logic, 3) PDF Free Download
Download Mathematical Logic (Oxford Texts in Logic, 3) 2007 PDF Free
Mathematical Logic (Oxford Texts in Logic, 3) 2007 PDF Free Download
Download Mathematical Logic (Oxford Texts in Logic, 3) PDF
Free Download Ebook Mathematical Logic (Oxford Texts in Logic, 3)