4 papers · 1 filter
Tameness, powerful images, and large cardinals
Will Boney, Michael Lieberman
We provide comprehensive, level-by-level characterizations of large cardinals, in the range from weakly compact to strongly compact, by closure properties of powerful images of acc…
Sizes and filtrations in accessible categories
Michael Lieberman, Jiří Rosický, Sebastien Vasey
Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from arXiv:1708.06782, we examine set-theor…
A category-theoretic characterization of almost measurable cardinals
Michael Lieberman
Through careful analysis of an argument of Brooke-Taylor and Rosicky, we show that the powerful image of any accessible functor is closed under colimits of -chains, a suffic…
Approximations of superstability in concrete accessible categories
Michael Lieberman, Jiri Rosicky
We generalize the constructions and results of Chapter 10 in Baldwin's "Categoricity" to coherent accessible categories with concrete directed colimits and concrete monomorphisms.…