Classicalities of Homotopy Type Theory

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What are statements of HoTT that are not provable therein and thus may or may not be true in specific models, specifically models in $(\infty,1)$- topoi? I've also seen the term "classicalities" being used for such statements.

The examples I've found are:

LEM, AC, Whitehead Principle, n-types covering.

I had also noted the statement that " A set-indexed wedge of circles is always a 1-type" but I seem to have lost that reference.

Are there any other such statements?