Answer by Holo for Is ZF + Def a conservative extension of ZFC+HOD? If not,...
Any model of ${\sf ZFC}+V=\sf HOD$ has an elementary equivalent pointwise definable model.If $M$ models $V=\sf HOD$, it has a parameter free definable well ordering, for each formula $φ$ consider the...
View ArticleIs ZF + Def a conservative extension of ZFC+HOD? If not, what are...
$\sf ZF + Def$ is the theory that extends $\mathcal L(=,\in)_{\omega_1,\omega}$ with axioms of $\sf ZF$ (written in $\mathcal L(=,\in)_{\omega, \omega}$) and the axiom of definability:-$\textbf{Define:...
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