Search Results: incompleteness-in-the-land-of-sets

Incompleteness in the Land of Sets

Author: Melvin Fitting

Publisher: N.A

ISBN: 9781904987345

Category: Mathematics

Page: 142

View: 1882

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.

The Bulletin of Symbolic Logic

Author: N.A

Publisher: N.A


Category: Electronic journals

Page: N.A

View: 7875

A Discourse and Register Analysis of the Prophetic Book of Joel

Author: Colin Toffelmire

Publisher: BRILL

ISBN: 9004325077

Category: Religion

Page: 242

View: 1385

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.

Der Gödelsche Beweis

Author: Ernest Nagel,James R. Newman

Publisher: de Gruyter Oldenbourg

ISBN: 9783486597264


Page: 110

View: 382

Spätestens seit Douglas R. Hofstadters "Gödel, Escher, Bach" ist der Name Gödel auch bei Nichtmathematikern bekannt geworden. 1931 hatte Kurt Gödel unter dem Titel "Über formal unterscheidbare Sätze der Principia Mathematica und verwandter Systeme" seinen Unvollständigkeitssatz publiziert. Nagel und Newman haben das Wesentliche an Gödels Ergebnissen für Nichtfachleute dargestellt. Die vorliegende 9. Auflage ist ein unveränderter Nachdruck der längst klassisch gewordenen Ausgabe von 1958.

Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 1948

Sets, Logic and Categories

Author: Peter J. Cameron

Publisher: Springer Science & Business Media

ISBN: 9781852330569

Category: Mathematics

Page: 182

View: 8772

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

Kurt Gödel

Jahrhundertmathematiker und großer Entdecker

Author: Rebecca Goldstein

Publisher: N.A

ISBN: 9783492249607


Page: 312

View: 7561

The law magazine and review : for both branches of the legal profession at home and abroad

Author: N.A

Publisher: N.A



Page: N.A

View: 8671

The Law Magazine and Review

A Quarterly Review of Jurisprudence

Author: N.A

Publisher: N.A


Category: Law

Page: N.A

View: 1180

Logic, Computation, Hierarchies

Author: Vasco Brattka,Hannes Diener,Dieter Spreen

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 1614519404

Category: Philosophy

Page: 424

View: 6816

Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.

Mengenlehre und ihre Logik

Author: Willard van Orman Quine

Publisher: Springer-Verlag

ISBN: 3322859436

Category: Mathematics

Page: 264

View: 6495

Law magazine and review0

Author: N.A

Publisher: N.A



Page: N.A

View: 9232

Modelling Soil Erosion by Water

Author: John Boardman,David Favis-Mortlock

Publisher: Springer Science & Business Media

ISBN: 3642589138

Category: Science

Page: 531

View: 945

TO THE MODEL EVALUATION 1. MODELLING SOIL EROSION BY WATER l 2 John Boardman and David Favis-Mortlock 1 School of Geography and Environmental Change Unit Mansfield Road University of Oxford Oxford OX1 3TB UK 2 Environmental Change Unit University of Oxford 5 South Parks Road Oxford OX1 3UB UK Introduction This volume is the Proceedings of the NATO Advanced Research Workshop 'Global Change: Modelling Soil Erosion by Water', which was held on II-14th September 1995, at the University of Oxford, UK. The meeting was also one of a series organised by the IGBP 1 GCTE Soil Erosion Network, which is a component of GCTE's Land Degradation Task (3.3.2) (Ingram et aI., 1996; Valentin, this volume). One aim of the GCTE Soil Erosion Network is to evaluate the suitability of existing soil erosion models for predicting the possible impacts of global change upon soil erosion. Due to the wide range of erosion models currently, in use or under development, it was decided to evaluate models in the following sequence Favis-Mortlock et al., 1996): • field-scale water erosion models • catchmenr-scale water erosion models • wind erosion models • models with a landscape-scale and larger focus. As part of this strategy, the first stage of the GCTE validation of field-scale erosion models was carried out at the Oxford NATO-ARW. I A list of Acronyms fonns Appendix A.

Satan, Cantor, And Infinity And Other Mind-bogglin

Author: Raymond M. Smullyan

Publisher: Knopf

ISBN: 0307819825

Category: Games & Activities

Page: 270

View: 7755

More than two hundred new and challenging logic puzzles—the simplest brainteaser to the most complex paradoxes in contemporary mathematical thinking—from our topmost puzzlemaster (“the most entertaining logician who ever lived,” Martin Gardner has called him). Our guide to the puzzles is the Sorcerer, who resides on the Island of Knights and Knaves, where knights always tell the truth and knaves always lie, and he introduces us to the amazing magic—logic—that enables to discover which inhabitants are which. Then, in a picaresque adventure in logic, he takes us to the planet Og, to the Island of Partial Silence, and to a land where metallic robots wearing strings of capital letters are noisily duplicating and dismantling themselves and others. The reader’s job is to figure out how it all works. Finally, we accompany the Sorcerer on an alluring tour of Infinity which includes George Cantor’s amazing mathematical insights. The tour (and the book) ends with Satan devising a diabolical puzzle for one of Cantor’s prize students—who outwits him! In sum: a devilish magician’s cornucopia of puzzles—a delight for every age and level of ability.

Capital in Disequilibrium

The Role of Capital in a Changing World

Author: Peter Lewin

Publisher: Routledge

ISBN: 1134756038

Category: Business & Economics

Page: 266

View: 8628

Drawing on the work of the Austrian School and its heirs, Capital in Disequilibrium develops a modern, systematic version of capital theory in order to suggest a new approach to the subject of economics. Original and provocative in his reflection, Lewin offers both a new approach and an accessible discussion of one of the most important, but also one of the most difficult, areas in economics.

Knowledge-Based Intelligent Information and Engineering Systems

10th International Conference, KES 2006, Bournemouth, UK, October 9-11 2006, Proceedings

Author: Bogdan Gabrys,Robert J. Howlett,L. C. Jain

Publisher: Springer Science & Business Media

ISBN: 3540465359

Category: Business & Economics

Page: 1300

View: 1940

The three volume set LNAI 4251, LNAI 4252, and LNAI 4253 constitutes the refereed proceedings of the 10th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2006, held in Bournemouth, UK in October 2006. The 480 revised papers presented were carefully reviewed and selected from about 1400 submissions. The papers present a wealth of original research results from the field of intelligent information processing.

Die Karte meiner Träume


Author: Reif Larsen,Manfred Allié

Publisher: N.A

ISBN: 9783596184446


Page: 435

View: 8722

Grundlagen der Mathematik I

Author: David Hilbert,Paul Bernays

Publisher: Springer-Verlag

ISBN: 3642868940

Category: Mathematics

Page: 480

View: 6022

Die Leitgedanken meiner Untersuchungen über die Grundlagen der Mathematik, die ich - anknüpfend an frühere Ansätze - seit 1917 in Besprechungen mit P. BERNAYS wieder aufgenommen habe, sind von mir an verschiedenen Stellen eingehend dargelegt worden. Diesen Untersuchungen, an denen auch W. ACKERMANN beteiligt ist, haben sich seither noch verschiedene Mathematiker angeschlossen. Der hier in seinem ersten Teil vorliegende, von BERNAYS abgefaßte und noch fortzusetzende Lehrgang bezweckt eine Darstellung der Theorie nach ihren heutigen Ergebnissen. Dieser Ergebnisstand weist zugleich die Richtung für die weitere Forschung in der Beweistheorie auf das Endziel hin, unsere üblichen Methoden der Mathematik samt und sonders als widerspruchsfrei zu erkennen. Im Hinblick auf dieses Ziel möchte ich hervorheben, daß die zeit weilig aufgekommene Meinung, aus gewissen neueren Ergebnissen von GÖDEL folge die Undurchführbarkeit meiner Beweistheorie, als irrtüm lich erwiesen ist. Jenes Ergebnis zeigt in der Tat auch nur, daß man für die weitergehenden Widerspruchsfreiheitsbeweise den finiten Stand punkt in einer schärferen Weise ausnutzen muß, als dieses bei der Be trachtung der elementaren Formallsmen erforderlich ist. Göttingen, im März 1934 HILBERT Vorwort zur ersten Auflage Eine Darstellung der Beweistheorie, welche aus dem HILBERTschen Ansatz zur Behandlung der mathematisch-logischen Grundlagenpro bleme erwachsen ist, wurde schon seit längerem von HILBERT ange kündigt.

Advanced Building Simulation

Author: Ali Malkawi,Godfried Augenbroe

Publisher: Routledge

ISBN: 1134357524

Category: Architecture

Page: 272

View: 7180

This book introduces recent advances in building simulation and outlines its historic development. Two important topics are described: uncertainty in simulation and coupled simulations, which are both closely linked to attempts to improve control and accuracy. This is followed by coverage of wind simulations and predictions, and then by an introduction to current systems and phenomenological modelling. Written by leading experts in the field both in the US and Europe, Advanced Building Simulation is an excellent graduate-level student textbook as well as a practical guide for architects, engineers and other construction professionals.

Find eBook