Q1: Assuming suitable consistency assumptions is the following consistent?
$ZFC+V=L+\text{Existence of class many weakly compact cardinals}$
Q2: What is the weakest known consistency assumption for proving the above consistency result?
2026-03-29 15:59:41.1774799981
How many weakly compact cardinals can L have?
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This is equiconsistent with $ZF+$ "There are class many weakly compacts." If $\kappa$ is weakly compact in $V$, then it is weakly compact in $L$. (See Jech chapter 17.) Thus the $L$ of any model of $ZF$ + "There are class many weakly compacts" is a model of $ZFC+V=L +$ "There are class many weakly compacts."