ask these questions because in my approach I can easily get a unique-ness result (its a different kind of system like quantum mechanics) which involves an infinite set of triples of global ordered finite additive propensity spaces, each closed under union etc, (ie all the non negative (x,y,z)xi>0,

omega=1, emptyset=0

where these frame functions must not only satisfy the same probabilistcrules on world, space F(x_1)+F(x_2)+F(x_3)=1, F(x4)=F(x1)+F(x3)=1-F(x_3)etc

1>F(xi)........i=1..6>0 F(omega)=1, F(emptyset)=0, F(x4)+F(x5)+F(x6)=2

but must respect the rank globally within each space if the any event of the 8 has the higher chance the function values must be greater, any of the 8 events have equal events including comparison between atomic events then the frame function values must be equal so if an atomic event is

x1=0.5, and x2=1/4, x3=1/4,

x4=x1or x3=1/4+1/2=3/4

x_5=x2\vee x3=1/4+1/4=1/2

x2=1/4=x3

implies F(x-3)=F(x2),

CH(x5=x2\vee x3)=x2+x3=1/4+1/4=1/2=CH(x1)\to F(x_1)=F(x_5=x2\vee x3)=F(x2)+F(x-3)=2F(x_2), F(x1, 1/2)+F(x2,1/4)+F(x3,1/4)=1 implis that as F(x_1,1/2)=2F(x_2;1/4), F(x_3 1/4)=F(x_2, 1/4) that 4F(x,2/14))=1, F(x3,1/4)=F(x2)=,1/4 F(x-1)=1/2

PR(omega)=1CH(x5))1/2=1/2CH(x_1)>CH(x_2)=1/4=1/4CH(x-3).CH(emptyset)=0\to F(\omega)=1> F(x4=x1\vee x3)=F(x1)+F(x_3)>F(x_5=x2\vee x3)=F(x2)=F(x3)=F(x1)=1/2>F(x2)=F(x-1)=1/4.>0,  but as F(x-1)=1/2 and F(x-3)=1/2 F(x43/4,x1\vee x3)=F(x1,1/2)+F(x3,1/4)=1/2=1/4=3/4

where this rank is global. and holds between distinct vectors the function Fis not explicitelt assumed to add if m=t, but it compares the any arbitary atomic events with an atomic or disjunctive event on another or the same space, where the sum of corresponding functions values if they are two disjunctive events ranked equal in chance(the disjunctiion are equal), must be such that Function values of the two disjunctions are equal which entails that the function values of those two pairs of disjunctive eventsums are indirectly,   but because of the equalities in the rank and the ability to compare atomic events with othjer atomic events, or atomic events on distinct worlds with disjunctive events,which will only be if the sum of the disjunct chances is equal to that atomic values chance,  that essentially gives rise to global additivity as the function values of the atomic event and the disjunction will be  tbe the same, iff only if the sum of two chance disjuncts  ahve sum equal tochance value of that atomic event, but that then the rank will assign same is the function value to the atomic on world 1 as to the disjunction in w3, but that is the function sum of the sum of its disjuncts in w-3by addivity within that world; effectilvelt ensuring that two disjunctive events which are (complementary in the sense that they sit on a different world, will have functions sums equal to the function values of  arbitary atomic events whenver and only if  hance value of the first CH(xt)=CH (x2)m+CH(x-3)mis equal to that chance sum the two disjuncts x1m x2m; so that F(x1+x2)=F(x1)+F(x2) where these re all atomic events, which due to the equalities in the rank eventually generalizing to events that do not event sit on a common space, they may be indifferent to an event s,x1=a, F(x1)=F(A) that is sit on a space with another event b=x2, F(b)=F(x2) where a and b lie together on the same world and are dijsoint, committing that function sum, value to the disunction due to the fact that first term and second term of each sum are the same the function sums must be, but that happens to the function value of the disjunctive events as a and b are disjoint, and whose chance values is also =x1+x2

F(a vee b)=F(a)+F(b)=F(x1)+F(x2)  where x2 or x3) has the same chance as tomic x-3

so that x-3=a\vb=a+b,a=x1, b=x2 implies x3=a+b=x1+x2

and F(x3)=F(a \vee b), bu t=F(a \vee b),=F(a)+F(b)=F(x1)+F(x2)

related to, or indifferent to the second, and third may be indifferent to the disjunction of these other events,

xi_m>xj_t iff F(x)>F(z)

 x_j_t=x^i_m,iff F(x)=F(xj), where

x_im