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Many people believe that the world is designed and created. However, this belief is not shared by everyone, so it's worth thinking about what this means. If the world is created, then it's likely to be the way it is because its Creator\footnote{Not everybody that believes that the world is created thinks that God created it. Still, I hope that they would agree that naming the creator of this world as \ghilimele{the Creator} is reasonable.} wanted it to have certain properties. In order to understand why our world works the way it does, one would need to understand the intent of its Creator. While that is interesting in itself, I will not try to pursue it here.  Let us consider the other case. If First, there are people that think it's unreasonable to believe that a world can exists without being created [TODO: insert reason here, something like "simply because the idea is outrageous"], and I agree with them. However, for this article, let us assume that  our world was not designed and created, created. If that's true  then there may be other worlds\footnote{We don't have any proof for the existence of other worlds, but one could expect them to exist for the same reason that ours exists. If ours has no reason at all for existing, which is likely if it is not created, then it's likely that other worlds would also not need any reason for existing and would simply be. However, for this paper it does not matter if there are other worlds or not and probably we wouldn't be able to tell if other worlds exist or not.}. Even if there are no other worlds, ours could have been different. We will denote by \definitie{possible worlds} these other worlds that either are or could have been. \section{Modelling possible worlds} 
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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, so let us also say that for sets of axioms having finite length we will break any ties by using the lexicographic order. For worlds having only sets of axioms of infinite length we can't use the same trick to break ties, but they all have the same length (countably infinite) so we will choose any such set of axioms and say that it's the best one. [TODO: Can I pick a minimum using inclusion? Can I use the fact that a finite set of 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. In the infinite  case and we  made an arbitrary decision in the infinite case, where decision, but then  the size cardinality  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?] anyway, even if there is some redundancy.  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}.