Algebraic set theory versus ETCS

Very much a preliminary draft, with errors!

This is a first cut at lining up and comparing various set theories and their models.

\[  \boxed{  \begin{array} {l|c|c|ccc}   \text{reference}  &  \text{Awodey}  &  \text{Leinster}  &  \text{SGL VI.10}    \\   \hline    \text{theories}  &  \text{BIST: Basic Intuitionistic Set Theory}  & \text{ETCS: Elementary Theory of the Category of Sets}   &  \text{RZC}  \\   \hline    \text{models}   &  \text{categories of classes}  &  &  \text{WPTNNC}   \\    \end{array}    }    \]

Awodey-Butz-Simpson-Streicher 2014 BIST APAL

https://www.sciencedirect.com/science/article/pii/S0168007213000730