About: Iterable cardinal

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In mathematics, an iterable cardinal is a type of large cardinal introduced by Gitman, and Sharpe and Welch, and further studied by Gitman and Welch. Sharpe and Welch defined a cardinal κ to be iterable if every subset of κ is contained in a weak κ-model M for which there exists an M-ultrafilter on κ which allows for wellfounded iterations by ultrapowers of arbitrary length.Gitman gave a finer notion, where a cardinal κ is defined to be α-iterableif ultrapower iterations only of length α are required to wellfounded. (By standard arguments iterability is equivalent to ω1-iterability.)

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  • In mathematics, an iterable cardinal is a type of large cardinal introduced by Gitman, and Sharpe and Welch, and further studied by Gitman and Welch. Sharpe and Welch defined a cardinal κ to be iterable if every subset of κ is contained in a weak κ-model M for which there exists an M-ultrafilter on κ which allows for wellfounded iterations by ultrapowers of arbitrary length.Gitman gave a finer notion, where a cardinal κ is defined to be α-iterableif ultrapower iterations only of length α are required to wellfounded. (By standard arguments iterability is equivalent to ω1-iterability.) (en)
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  • In mathematics, an iterable cardinal is a type of large cardinal introduced by Gitman, and Sharpe and Welch, and further studied by Gitman and Welch. Sharpe and Welch defined a cardinal κ to be iterable if every subset of κ is contained in a weak κ-model M for which there exists an M-ultrafilter on κ which allows for wellfounded iterations by ultrapowers of arbitrary length.Gitman gave a finer notion, where a cardinal κ is defined to be α-iterableif ultrapower iterations only of length α are required to wellfounded. (By standard arguments iterability is equivalent to ω1-iterability.) (en)
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  • Iterable cardinal (en)
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