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