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supercompact

Jednojezični primeri (nisu ih verifikovali PONS urednici)

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Finding a canonical inner model for supercompact cardinals is one of the major problems of inner model theory. en.wikipedia.org

A measurable limit of strongly compact cardinals is strongly compact, but the least such limit is not supercompact. en.wikipedia.org

Some set theorists conjecture that existence of a strongly compact cardinal is equiconsistent with that of a supercompact cardinal. en.wikipedia.org

However, a proof is unlikely until a canonical inner model theory for supercompact cardinals is developed. en.wikipedia.org

In a supercompact space (or any continuous image of one), the cluster point of any countable subset is the limit of a nontrivial convergent sequence. en.wikipedia.org

Conversely, many (but not all) compact spaces are supercompact. en.wikipedia.org

The relationship is analogous to that of extendible versus supercompact cardinals. en.wikipedia.org

He proved that the least strongly compact cardinal can be equal to the least measurable cardinal or to the least supercompact cardinal (but not at the same time). en.wikipedia.org

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