Rob Bensinger comments on Biextensional Equivalence

[Rob Bensinger]

An example of frames that are biextensionally equivalent to $C_1$:

$\begin{array}{cc}& \left(\begin{array}{cc}{w}_8& w_9\\ w_{10}& w_{11}\\ w_8& w_9\\ w_{10}& w_{11}\end{array}\right)\end{array}\simeq \begin{array}{cc}& \left(\begin{array}{cc}{w}_8& w_9\\ w_{10}& w_{11}\\ w_8& w_9\end{array}\right)\end{array}\simeq \begin{array}{cc}& \left(\begin{array}{cc}{w}_8& w_9\\ w_{10}& w_{11}\\ w_{10}& w_{11}\end{array}\right)\end{array}\simeq \begin{array}{cc}& \left(\begin{array}{cc}{w}_8& w_9\\ w_{10}& w_{11}\end{array}\right)\end{array}$

… or any frame that enlarges one of those four frames by adding extra copies of any of the rows and/​or columns.

[ESRogs]

This is helpful. Thanks!

[Rob Bensinger]

Scott’s post explaining the relationship between $C_0$ and $C_1$ exists as of now: Functors and Coarse Worlds.