On Jónsson cardinals with uncountable cofinality
For a regular cardinal κ a Jónsson model of size κ+ is presented. We notice that every singular Jónsson cardinal κ with uncountable cofinality is the limit of some continuous sequence of smaller Jónsson cardinals. An analogous statement holds if κ is an inaccessible Jónsson cardinal unless κ is Mahlo. But we prove that the first Mahlo cardinal cannot be Jónsson. Some additional remarks are included.
KeywordsRegular Cardinal Measurable Cardinal Elementary Embedding Generic Filter Inaccessible Cardinal
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