Titlebook: Introduction to Cardinal Arithmetic; M. Holz,K. Steffens,E. Weitz Textbook 1999 Springer Basel AG 1999 Addition.Alephs.Arithmetic.Axiom of

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M. Holz,K. Steffens,E. Weitzquantum optics. It also provides an expanded treatment of the minimum-coupling Hamiltonian and a simple derivation of the Gross-Pitaevskii equation, an important gateway to research in ultracold atoms and molecules. .978-3-642-09352-4978-3-540-74211-1

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M. Holz,K. Steffens,E. Weitzquantum optics. It also provides an expanded treatment of the minimum-coupling Hamiltonian and a simple derivation of the Gross-Pitaevskii equation, an important gateway to research in ultracold atoms and molecules. .978-3-642-09352-4978-3-540-74211-1

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Applications of pcf-Theory,As a first application of pcf-theory, we will prove in this section two estimates for cardinal numbers. Initially, if . is a limit ordinal and . is a cardinal with . < ℵ. then ..

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M. Holz,K. Steffens,E. WeitzSelf-contained introduction to cardinal arithmetic which also includes pcf theory.Gives a relatively complete survey of results provable in ZFC.Includes supplementary material: