Sampling Subsets from a Set

Hello community,
I have a conceptual modelling question - I will attempt to abstract away as much as the details as possible.

Assume, you have a set \mathcal{T}. I wish to define a prior on the subsets of \mathcal{T}. Then, my paramater becomes simplex[$2^|T|$] theta (size equalling the powerset of \mathcal{T}).
The way I want to define this prior is via Bernoulli trials - for each element of \mathcal{T} perform a Bernoulli trial with success probability p and keep the ones that succeed.

What is a way to implement this distribution in STAN?

Can you provide more detail on what you mean here? How do you define p? And when you say “keep the ones that succeed”, how do you intend to define a prior from that?

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