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\section {Modelling from inside}  We could also completely avoid the axiom set encoding problem by talking only about worlds which could contain intelligent beings and talking about how the intelligent beings would model their world. Let Even more, let  us note that if those include only world where there  intelligent beings are would be  similar enough to us in that they can use logic  and the mathematics, but they wouldn't be able to process an infinite amount of that in a finite time. Let us note that in worlds with an infinite  optimal set of axioms for their world is infinite then these intelligent beings  they will never have a complete description of how their world works, but they will be able to build better and better models. Let us assume that those intelligent beings are continuously trying to find better models for their world and that they are reasonably efficient at this.