Hallo! Tracked shipping to Netherlands with Delivery Duty Paid for just €7 

Ship to
Netherlands
0

My Account

  • argentina
  • chile
  • colombia
  • españa
  • méxico
  • perú
  • estados unidos
  • internacional

menu

Select your country

Americas

Europe

Rest of the world

portada Incompleteness for Higher-Order Arithmetic: An Example Based on Harrington's Principle
Type
Physical Book
Author
Publisher
Language
English
Pages
122
Format
Paperback
Dimensions
23.4x15.6x0.8 cm
Weight
0.20 kg.
ISBN13
9789811399480
Categories

Incompleteness for Higher-Order Arithmetic: An Example Based on Harrington's Principle

Yong Cheng (Author) · Springer · Paperback

Incompleteness for Higher-Order Arithmetic: An Example Based on Harrington's Principle - Cheng, Yong

Cheaper New Book Imported to Netherlands
Delivery: 30 Sep - 07 Oct Shipping: 16 to 20 business days.
€ 61,71
Faster New Book Imported to Netherlands
Delivery: 25 Sep - 29 Sep Shipping: 13 to 14 business days.
€ 75,74
Import costs and 9% BTW included in the price ✅
€ 61,71

Choose the list to add your product or create one New List

Go to My Wishlists
Calculate shipping cost

Synopsis "Incompleteness for Higher-Order Arithmetic: An Example Based on Harrington's Principle"

Gödel's true-but-unprovable sentence from the first incompleteness theorem is purely logical in nature, i.e. not mathematically natural or interesting. An interesting problem is to find mathematically natural and interesting statements that are similarly unprovable. A lot of research has since been done in this direction, most notably by Harvey Friedman. A lot of examples of concrete incompleteness with real mathematical content have been found to date. This brief contributes to Harvey Friedman's research program on concrete incompleteness for higher-order arithmetic and gives a specific example of concrete mathematical theorems which is expressible in second-order arithmetic but the minimal system in higher-order arithmetic to prove it is fourth-order arithmetic.This book first examines the following foundational question: are all theorems in classic mathematics expressible in second-order arithmetic provable in second-order arithmetic? The author gives a counterexample for this question and isolates this counterexample from the Martin-Harrington Theorem in set theory. It shows that the statement "Harrington's principle implies zero sharp" is not provable in second-order arithmetic. This book further examines what is the minimal system in higher-order arithmetic to prove the theorem "Harrington's principle implies zero sharp" and shows that it is neither provable in second-order arithmetic or third-order arithmetic, but provable in fourth-order arithmetic. The book also examines the large cardinal strength of Harrington's principle and its strengthening over second-order arithmetic and third-order arithmetic.

Customers reviews

More customer reviews
  • 0% (0)
  • 0% (0)
  • 0% (0)
  • 0% (0)
  • 0% (0)

Frequently Asked Questions about the Book

Is the book original?

All books in our catalog are Original.

In what language is the book written?

The book is written in English.

What is the format of this book?

The binding of this edition is Paperback.

Questions and Answers about the Book

Do you have a question about the book? Login to be able to add your own question.

Opinions about Bookdelivery

More customer reviews