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

1. Dec 2, 2011

### jgens

1. The problem statement, all variables and given/known data

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

2. Relevant equations

N/A

3. 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!

2. Dec 2, 2011

### 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.