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Let us restrict the possible worlds term to the worlds where we can make predictions and let us use only sets of axioms that allow predictions. As mentioned above, for a given world, a good set of axioms is one which allows us to make all possible correct predictions for that world (statistical or not). Using only good sets of axioms solves the \ghilimele{too-general problem} since such a set would describe its possible worlds in a way that does not leave out important things. Still, there is nothing that prevents such a set from going into too much details.  Let us chose any formalism for specifying axioms that uses a finite alphabet and let us choose an arbitrary order relation on that  alphabet. Also, we will only consider axiom sets which, when written on an infinite paper, use at most a countable number of symbols.  Then, for each possible world, we could say that the best set of axioms is the smallest good one, smallest being defined as having the smallest length when written on (possibly infinite)  paper. This is not a well defined notion notion, so let us also say that  fora few reasons. First, there could be multiple  sets with the smallest of axioms having finite  length(one obvious case is given by reordering the axioms). In such a case, we could define an order for the symbols that  we are will break any ties by  usingin our formalism and we could pick the system with the smallest length and which is the smallest in  the lexicographic order. Second, there could be systems For worlds having only sets  of axioms of infinite length [TODO: These we  can't really be sorted. I can have an infinite sequence of sets of axioms s1, s2, ... where each element is smaller than its predecessor, use the same trick to break ties,  but which has no limit. I think I can't reject they  allsystems which include other systems, I may again  havean infinite chain. I can reject systems for which some part is implied by a smaller finite part in another system and  the reminder is the same.] For this, same length (countably infinite) so  we will only consider systems which, when written on an infinite paper, use a countable number choose any such set  of symbols. This means axioms and say  that all will have it's  the same length, but we can still best one. [TODO: Can I pick a minimum using inclusion? Can I  use the lexicographic order to compare them. We will ignore systems which need an uncountable fact that a finite  set of symbol places. axioms implies a larger set and replace them?].  With an axiom system chosen in this way we would also solve the \ghilimele{too-specific problem} in the finite case and made an arbitrary decision in the infinite case, where the size of the axiom set matches the complexity of the world anyway.  [TODO: I only solved it for finite systems. Do I also need to solve it for infinite systems?]since we would remove any axiom that's not absolutely needed.  If $U$ is an universe and $A$ is the smallest set of predictive axioms as described above, then we would say than $A$ is the \definitie{optimal set of axioms for $U$}. If $A$ is a set of axioms which is optimal for some universe $U$ then we say that $A$ is an \definitie{optimal set of axioms}.