I think also that it would be great to show if this theory applied to the actual physical universe in which we exist, or it just describes a type of mathematical objects as sets or groups.
If it apllied to physical universe, we can’t ignore the question of its origin, as it will have direct correlation with its observed complexity. If mathematical universe hypothesis (MUH) is true, and all math objects exists, than more complex objects should dominate. But it contradict our expiriences and Occam razor. There is a need to bring order to all possible universes. And here Logical universes hypothesis (LUH) helps. It claims that existing math objects following from simple to more complex in logical order, like 1,2,3. In that case simplest math objects appear first—and we get support to your Axiome 3.
I think also that it would be great to show if this theory applied to the actual physical universe in which we exist, or it just describes a type of mathematical objects as sets or groups.
If it apllied to physical universe, we can’t ignore the question of its origin, as it will have direct correlation with its observed complexity. If mathematical universe hypothesis (MUH) is true, and all math objects exists, than more complex objects should dominate. But it contradict our expiriences and Occam razor. There is a need to bring order to all possible universes. And here Logical universes hypothesis (LUH) helps. It claims that existing math objects following from simple to more complex in logical order, like 1,2,3. In that case simplest math objects appear first—and we get support to your Axiome 3.
I explored different ways of the universe origin and its correlation with observation here: http://lesswrong.com/lw/nw7/the_map_of_ideas_how_the_universe_appeared_from/