ⓘ Iterable cardinal. In mathematics, an iterable cardinal is a type of large cardinal introduced by Gitman, and Sharpe and Welch, and further studied by Gitman an ..

                                     

ⓘ Iterable cardinal

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 -iterable if ultrapower iterations only of length α are required to wellfounded.

                                     
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  • totally ineffable cardinals remarkable cardinals α - Erdos cardinals for countable α 0 not a cardinal γ - iterable γ - Erdos cardinals for uncountable
  • In mathematics, a Mahlo cardinal is a certain kind of large cardinal number. Mahlo cardinals were first described by Paul Mahlo  1911, 1912, 1913 As
  • whose elements are in M. Huge cardinals were introduced by Kenneth Kunen  1978 In what follows, jn refers to the n - th iterate of the elementary embedding
  • mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This
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  • the mathematical discipline of set theory, a cardinal characteristic of the continuum is an infinite cardinal number that may consistently lie strictly between
  • showed that iterated forcing can construct models where Martin s axiom holds and the continuum is any given regular cardinal In iterated forcing, one
  • Cardinal is the second studio album by American rock band Pinegrove, released February 12, 2016 on Run for Cover. Pinegrove formed in Montclair, New Jersey
  • an added condition of iterability referring to the existence of wellfounded iterated ultrapowers a mouse is then an iterable premouse. The notion of
  • alternative to large cardinal axioms. The Fundamental Theorem of Proper Forcing, due to Shelah, states that any countable support iteration of proper forcings