Collection of Well-Formed Formulas with no Equivalent, Independent Subset

[jgens]

Homework Statement

Find a collection of well-formed formulas Ʃ such that Ʃ has no independent equivalent subset.

Homework Equations

N/A

The Attempt at a Solution

So far I have been able to show that Ʃ must be infinite. However, after this, I get stuck. Could anyone give me a hint on how to construct such a Ʃ?

Thanks!

 

[jgens]

I figured it out. If we take $\Sigma = \{A_1, A_1 \wedge A_2, \dots, A_1 \wedge \cdots \wedge A_n, \dots\}$, then that should work.