Incompleteness in the Land of Sets

Incompleteness in the Land of Sets
Author: Melvin Fitting
Publsiher: Unknown
Total Pages: 142
Release: 2007
Genre: Mathematics
ISBN: 1904987346

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Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of Godel, Church, Rosser, and Post. This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. Godel numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to Godel's Second Incompleteness Theorem. Exercises are scattered throughout.

Raymond Smullyan on Self Reference

Raymond Smullyan on Self Reference
Author: Melvin Fitting,Brian Rayman
Publsiher: Springer
Total Pages: 195
Release: 2018-01-11
Genre: Philosophy
ISBN: 9783319687322

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This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.

Universality in Set Theories

Universality in Set Theories
Author: Manuel Bremer
Publsiher: Walter de Gruyter
Total Pages: 125
Release: 2013-05-02
Genre: Philosophy
ISBN: 9783110326109

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The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?

United States Congressional Serial Set

United States Congressional Serial Set
Author: Anonim
Publsiher: Unknown
Total Pages: 135
Release: 2022
Genre: Electronic Book
ISBN: UCAL:B3990225

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Forever Undecided

Forever Undecided
Author: Raymond M. Smullyan
Publsiher: Knopf
Total Pages: 257
Release: 2012-07-04
Genre: Mathematics
ISBN: 9780307962461

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Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!

The Construction of Property

The Construction of Property
Author: Amnon Lehavi
Publsiher: Cambridge University Press
Total Pages: 351
Release: 2013-06-20
Genre: Law
ISBN: 9781107035386

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Presents a structural and institutional theory of property and examines property regimes, protagonists of property and the challenges of globalisation.

Godel s Incompleteness Theorems

Godel s Incompleteness Theorems
Author: Raymond M. Smullyan
Publsiher: Oxford University Press
Total Pages: 160
Release: 1992-08-20
Genre: Mathematics
ISBN: 9780190281441

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Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

The Impact of Incomplete Contracts on Economics

The Impact of Incomplete Contracts on Economics
Author: Philippe Aghion,Mathias Dewatripont,Patrick Legros,Luigi Zingales
Publsiher: Oxford University Press
Total Pages: 224
Release: 2015-12-22
Genre: Business & Economics
ISBN: 9780190259013

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The 1986 article by Sanford J. Grossman and Oliver D. Hart titled "A Theory of Vertical and Lateral Integration" has provided a framework for understanding how firm boundaries are defined and how they affect economic performance. The property rights approach has provided a formal way to introduce incomplete contracting ideas into economic modeling. The Impact of Incomplete Contracts on Economics collects papers and opinion pieces on the impact that this property right approach to the firm has had on the economics profession.

Serial set no 0 3099

Serial set  no 0 3099
Author: Anonim
Publsiher: Unknown
Total Pages: 135
Release: 1892
Genre: Electronic Book
ISBN: UCAL:$B636043

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G del s Theorem

G  del s Theorem
Author: Torkel Franzén
Publsiher: CRC Press
Total Pages: 182
Release: 2005-06-06
Genre: Mathematics
ISBN: 9781439876923

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"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel

A Discourse and Register Analysis of the Prophetic Book of Joel

A Discourse and Register Analysis of the Prophetic Book of Joel
Author: Colin Toffelmire
Publsiher: BRILL
Total Pages: 242
Release: 2016-07-04
Genre: Religion
ISBN: 9789004325074

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In A Discourse and Register Analysis of the Prophetic Book of Joel, Colin M. Toffelmire presents a thorough analysis of the text of Joel from the perspective of Systemic Functional Linguistics.

China s Rural Areas

China s Rural Areas
Author: China Development Research Foundation
Publsiher: Taylor & Francis
Total Pages: 382
Release: 2017-04-21
Genre: Social Science
ISBN: 9781351784849

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The prosperity of China’s people has advanced very much in recent decades. However, in many respects China is still a developing country, and this is especially true of rural areas where economic progress has not been as marked as in urban areas and where many people still live in relative poverty. The Chinese government recognizes that more hard work is needed in order to improve prosperity in the countryside. This book provides a systematic and comprehensive analysis of the situation in China’s rural areas, assesses the effectiveness or otherwise of current policies, and puts forward proposals for further development. Subjects covered include the changing population profile of rural areas, land ownership, agricultural improvements, and local self-government.

Proceedings of the 23rd International Symposium on Advancement of Construction Management and Real Estate

Proceedings of the 23rd International Symposium on Advancement of Construction Management and Real Estate
Author: Fenjie Long,Sheng Zheng,Yuzhe Wu,Gangying Yang,Yan Yang
Publsiher: Springer Nature
Total Pages: 1398
Release: 2021-02-02
Genre: Business & Economics
ISBN: 9789811539770

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This book presents the proceedings of CRIOCM2018, 23rd International Symposium on Advancement of Construction Management and Real Estate, sharing the latest developments in real estate and construction management around the globe. The conference was organized by the Chinese Research Institute of Construction Management (CRIOCM) working in close collaboration with Guizhou Institute of Technology (GIT). Written by international academics and professionals, the proceedings discuss the latest achievements, research findings and advances in frontier disciplines in the field of construction management and real estate. Covering a wide range of topics, including New-type urbanization, land development and land use, urban planning and infrastructure construction, housing market and housing policy, real estate finance and investment, new theories and practices on construction project management, smart city, BIM technologies and applications, construction management in big data era, green architecture and eco-city, rural rejuvenation and eco-civilization, other topics related to construction management and real estate, the discussions provide valuable insights into the advancement of construction management and real estate in the new era. The book is an outstanding reference resource for academics and professionals alike.

The New Law of Land Registration

The New Law of Land Registration
Author: Elizabeth Cooke
Publsiher: Bloomsbury Publishing
Total Pages: 315
Release: 2003-09-17
Genre: Law
ISBN: 9781847316868

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This book is an examination of the law of land registration in England and Wales, in the light of the Land Registration Act 2002, and in particular at the way land registration is influenced by, and in turn influences, the evolution of land law as a whole. It examines the legal problems that have arisen in connection with land registration and considers the effect of the 2002 statute, drawing extensively upon the law in other jurisdictions and considering possibilities for future development. This is a book which will be essential reading for students, their teachers, and practitioners who will have to grapple with the intricacies of the new Act when it comes into force.

The G delian Puzzle Book

The G  delian Puzzle Book
Author: Raymond M. Smullyan
Publsiher: Courier Corporation
Total Pages: 240
Release: 2013-08-21
Genre: Mathematics
ISBN: 9780486315775

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These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic necessary.