User:Vel!/FOST

Roll over, Turing machines! It's time for some first-order set theory.

On this page, you can contribute FOST formulas. Discussions about specific formulas are welcome on this page (use the talk page for general discussion). Here are some conventions I suggest:


 * "T" represents a "target." If you're building a formula designed to construct a certain set, the formula should force the value of T. Setting T to 1 will make it the output of the formula.
 * When appropriate, use letters instead of numbers.
 * You can make shortcuts to make the formulas more readable.

Empty set
¬∃x: x ∈ T

This formula forces T to be the empty set.

Subset
¬∃x: (x ∈ a) ∧ (¬x ∈ b)

This formula forces a to be a subset of b.