\setlength{\parindent}{0pt} \setlength{\parskip}{1em} \DeclareMathOperator{\Con}{Con} \newcommand\ZFC{\textsf{ZFC}} \newcommand\zfc{\ZFC} \newcommand\zf{\textsf{ZF}} \newcommand\CH{\textsf{CH}} \newcommand\ch{\CH} \newcommand\ac{\textsf{AC}} \newcommand\gch{\textsf{GCH}} \newcommand\psa{\textsf{PSA}} \newcommand\delz{\glsref[delz_symbol]{\Delta_0}} \newcommand\delzt{\glsref[delz_symbol]{\Delta_0^T}} \DeclareMathOperator{\dom}{dom} \DeclareMathOperator{\range}{range} \DeclareMathOperator{\Ord}{Ord} \newcommand\pio{\glsref[Pi0Sigma1_symbol]{\Pi_1}} \newcommand\sigo{\glsref[Pi0Sigma1_symbol]{\Sigma_1}} \newcommand\delot{\glsref[delot_symbol]{\Delta_0^T}} \DeclareMathOperator{\Fmlinternal}{Fml} \newcommand\Fml{\glsref[Fml_symbol]{\Fmlinternal}} \DeclareMathOperator{\tcl}{tcl} \newcommand\dgen[1][\mathcal{D}]{\glsref[Dgen]{$#1$-generic}} \DeclareMathOperator{\Fn}{Fn} \DeclareMathOperator{\Name}{Name} \DeclareMathOperator{\val}{val} \newcommand\incomp{\glsref[incomp]{\perp}} \DeclareMathOperator{\up}{up} \newcommand\fl{\glsref[fl]{\mathcal{L}_{\text{forcing}}}} \newcommand\forces{\glsref[forcing_symbol]{\Vdash}} \newcommand\syn{\vdash} \DeclareMathOperator{\cfinternal}{cf} \newcommand\cf{\glsref[cofinal]{\cfinternal}} \DeclareMathOperator{\olinternal}{OL} \newcommand\OL{\glsref[ol_symbol]{\olinternal}}