Ordinal notation: Mathematical Logic, Set Theory, Ordinal Number, Recursive Set, Well-Order, Church–Kleene Ordinal, Natural Number, Ordinal Arithmetic, Recursively Enumerable Set - Softcover

 
9786130338558: Ordinal notation: Mathematical Logic, Set Theory, Ordinal Number, Recursive Set, Well-Order, Church–Kleene Ordinal, Natural Number, Ordinal Arithmetic, Recursively Enumerable Set
Softcover
ISBN 10: 6130338554 ISBN 13: 9786130338558
Publisher: Betascript Publishing, 2010

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language. There are many such schemes of ordinal notations, including schemes by Wilhelm Ackermann, Heinz Bachmann, Buchholz, Georg Cantor, Solomon Feferman, Gerhard Jäger, Isles, Pfeiffer, Wolfram Pohlers, Kurt Schütte, Gaisi Takeuti (called ordinal diagrams), Oswald Veblen. Given such a scheme, one should be able to define a recursive well-ordering of a subset of the natural numbers by associating a natural number with each finite sequence of symbols via a Gödel numbering. Stephen Cole Kleene has a system of notations, called Kleene''s O, which includes ordinal notations but it is not as well behaved as the other systems described here.

"synopsis" may belong to another edition of this title.

Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language. There are many such schemes of ordinal notations, including schemes by Wilhelm Ackermann, Heinz Bachmann, Buchholz, Georg Cantor, Solomon Feferman, Gerhard Jäger, Isles, Pfeiffer, Wolfram Pohlers, Kurt Schütte, Gaisi Takeuti (called ordinal diagrams), Oswald Veblen. Given such a scheme, one should be able to define a recursive well-ordering of a subset of the natural numbers by associating a natural number with each finite sequence of symbols via a Gödel numbering. Stephen Cole Kleene has a system of notations, called Kleene''s O, which includes ordinal notations but it is not as well behaved as the other systems described here.

"About this title" may belong to another edition of this title.

Publisher
Betascript Publishing
Publication date
2010
Language
English
ISBN 10 
6130338554
ISBN 13 
9786130338558
Binding
Tapa blanda
Number of pages
68
Editor
Surhone Lambert M., Timpledon Miriam T., Marseken Susan F.