partition axiom 2 (PA2):

C,B in A s.t. C">"B => there exists {E1,..,En} of O s.t. A">"B union Ei forall i

PA2 =>

• {w} ~ empty set
• atomlessness

Proposition:
"=>" QP => ( PA2 <=> fine /\ tight)

Theorem:
"=>" QP /\ PA2 <=> there exists P on (O,2^O) s..t

• A"=>"B <=> P(A)=>P(B)
• forall A in 2^O, forall v in [0,1] there exists B subset A s.t. P(B)=vP(A)