I've been looking into the idea of large cardinals recently, and I found this question in particular to be interesting.
Large Cardinals Ordered by Cardinality of Least Instance
The most popular answer to this question goes very in depth about the ordering of cardinality for large cardinals, and it made me think of a few questions.
The answer mentions stationary transcendence and measurable transcendence, and talks about how they are two different magnitudes. I don't know about stationary, but measurable transcendence seems to have something to do with measurable cardinals, so I am curious. Is there something akin to "extendable transcendence" (in relation to extendable cardinals), and could there theoretically be larger levels of transcendence, as you get into larger and larger cardinals.