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We consider a weak version of Schindler’s remarkable cardinals that may fail to be 
${{\rm{\Sigma }}_2}$-reflecting. We show that the 
${{\rm{\Sigma }}_2}$-reflecting weakly remarkable cardinals are exactly the remarkable cardinals, and that the existence of a non-
${{\rm{\Sigma }}_2}$-reflecting weakly remarkable cardinal has higher consistency strength: it is equiconsistent with the existence of an ω-Erdős cardinal. We give an application involving gVP, the generic Vopěnka principle defined by Bagaria, Gitman, and Schindler. Namely, we show that gVP + “Ord is not 
${{\rm{\Delta }}_2}$-Mahlo” and 
${\text{gVP}}(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\Pi } _1 )$ + “there is no proper class of remarkable cardinals” are both equiconsistent with the existence of a proper class of ω-Erdős cardinals, extending results of Bagaria, Gitman, Hamkins, and Schindler.
