عنوان
پدید آورنده
موضوع
رده
QA9.54 .C54 2019eb
QA9
.
54
.
C54
2019eb
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9789811399497
(Number (ISBN
9789811399503
(Number (ISBN
9789811399510
(Number (ISBN
9811399492
(Number (ISBN
9811399506
(Number (ISBN
9811399514
Erroneous ISBN
9789811399480
Erroneous ISBN
9811399484
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Incompleteness for higher-order arithmetic :
General Material Designation
[Book]
Other Title Information
an example based on Harrington's principle /
First Statement of Responsibility
Yong Cheng.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Singapore :
Name of Publisher, Distributor, etc.
Springer,
Date of Publication, Distribution, etc.
[2019]
Date of Publication, Distribution, etc.
©2019
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
SERIES
Series Title
SpringerBriefs in mathematics,
ISSN of Series
2191-8198
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
Intro; Preface; Acknowledgements; Contents; 1 Introduction and Preliminaries; 1.1 Preliminaries; 1.1.1 Basics of Incompleteness; 1.1.2 Basics of Reverse Mathematics; 1.1.3 Overview of Incompleteness for Higher-Order Arithmetic; 1.1.4 Basics of Set Theory; 1.2 Introduction; References; 2 A Minimal System; 2.1 Preliminaries; 2.1.1 Almost Disjoint Forcing; 2.1.2 The Large Cardinal Notion 0; 2.1.3 Remarkable Cardinal; 2.2 The Strength of Z2+ Harrington's Principle; 2.3 The Strength of Z3+ Harrington's Principle; 2.4 Z4 + Harrington's Principle Implies that 0 Exists; References
Text of Note
3 The Boldface Martin-Harrington Theorem in Z23.1 The Boldface Martin Theorem in Z2; 3.2 The Boldface Harrington Theorem in Z2; References; 4 Strengthenings of Harrington's Principle; 4.1 Overview; 4.2 Harrington's Club Shooting Forcing; 4.3 The Strength of Z2 + HP(); 4.4 Subcomplete Forcing; 4.5 The Strength of Z3 + HP(); References; 5 Forcing a Model of Harrington's Principle Without Reshaping; 5.1 Introduction; 5.2 The Notion of Strong Reflecting Property for L-Cardinals; 5.3 Baumgartner's Forcing; 5.4 The First Step; 5.5 The Second Step; 5.6 The Third Step; 5.7 The Fourth Step; References
0
8
SUMMARY OR ABSTRACT
Text of Note
The book examines the following foundation question: are all theorems in classic mathematics which are expressible in second order arithmetic provable in second order arithmetic? In this book, the author gives a counterexample for this question and isolates this counterexample from Martin-Harrington theorem in set theory. It shows that the statement "Harrington's principle implies zero sharp" is not provable in second order arithmetic. The book also examines what is the minimal system in higher order arithmetic to show that Harrington's principle implies zero sharp and the large cardinal strength of Harrington's principle and its strengthening over second and third order arithmetic.
ACQUISITION INFORMATION NOTE
Source for Acquisition/Subscription Address
Springer Nature
Stock Number
com.springer.onix.9789811399497
OTHER EDITION IN ANOTHER MEDIUM
Title
Incompleteness for Higher-Order Arithmetic : An Example Based on Harrington's Principle.
International Standard Book Number
9789811399480
TOPICAL NAME USED AS SUBJECT
Incompleteness theorems.
Incompleteness theorems.
(SUBJECT CATEGORY (Provisional
MAT018000
PBC
PBC
PBCD
DEWEY DECIMAL CLASSIFICATION
Number
511
.
3
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA9
.
54
Book number
.
C54
2019eb
PERSONAL NAME - PRIMARY RESPONSIBILITY
Cheng, Yong
ORIGINATING SOURCE
Date of Transaction
20200823231556.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
