	Since On⊂L⊆V, properties of ordinals that depend on the absence of a function or other structure (i.e. Π formulas) are preserved when going down from V to L. Hence initial ordinals of cardinals remain initial in L. Regular ordinals remain regular in L. Weak limit cardinals become strong limit cardinals in L because the generalized continuum hypothesis holds in L. Weakly inaccessible cardinals become strongly inaccessible. Weakly Mahlo cardinals become strongly Mahlo. And more generally, any large cardinal property weaker than 0 (see the list of large cardinal properties) will be retained in L.