Oct 22

Computability: Computable Functions, Logic, and the

Format: Hardcover

Language: English

Format: PDF / Kindle / ePub

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NBG’s principle of class comprehension is predicative; i.e. quantified variables in the defining formula can’t range over proper classes but range only over sets, and we get a conservative extension of ZFC (nothing in the language of sets can be proved in NBG which can’t already be proved in ZFC). For instance, the minimal closure of an operation on a set is ordinarily defined as the intersection of all sets that are closed under applications of the operation. It is specifically defined as the positive square root of the variance (σ 2); in symbols, σ 2 = Σ(x i − μ) 2 / n, where Σ is a compact notation used to indicate that as the index (i) changes from 1...

Pages: 384

Publisher: Advanced Reasoning Forum (June 1, 2008)

ISBN: 098155072X

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