Combinatorial number theory : a treatise on growth, based on the Goodstein-Skolem hierarchy, including a critique of non-constructive or first order logic
著者
書誌事項
Combinatorial number theory : a treatise on growth, based on the Goodstein-Skolem hierarchy, including a critique of non-constructive or first order logic
E. Mellen Press, c1994
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注記
Includes bibliographical references (p. 411-420) and indexes
内容説明・目次
内容説明
The science of growth is arithmetic in constitution. By drawing on the technical literature (from the 18th century onward), this monograph seeks to expose the deep combinatorial foundations of the theory. It contains ideas of mathematical logic, including the finitary concept of normal tree, and the feather diagram of a hierarchy. Central to the book is a proof of Birkhoff's descending chain condition, as it arises in a diagonalization of mathematical induction. At no point is the vexed axiomatic of choice used. Contingent on the above reductions are, for example, an acceptable Gentzen-type proof of freedom from contradiction for first-order arithmetic and combinatorial relations apparent at the centre of logic. These include an infinite product first studied by A. Cayley, and a subtle property of the Cantor normal form, contained in an exponential identity of G. Polya.
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