# The large cardinals between supercompact and almost-huge

@article{Perlmutter2015TheLC, title={The large cardinals between supercompact and almost-huge}, author={Norman Lewis Perlmutter}, journal={Archive for Mathematical Logic}, year={2015}, volume={54}, pages={257-289} }

AbstractI analyze the hierarchy of large cardinals between a supercompact cardinal and an almost-huge cardinal. Many of these cardinals are defined by modifying the definition of a high-jump cardinal. A high-jump cardinal is defined as the critical point of an elementary embedding $${j: V \to M}$$j:V→M such that M is closed under sequences of length $${\sup\{{j(f)(\kappa)\,|\,f: \kappa \to \kappa}\}}$$sup{j(f)(κ)|f:κ→κ}. Some of the other cardinals analyzed include the super-high-jump cardinals…

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