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Random constructions imply symmetry
Last modified: 2014-02-07
Abstract
We will argue for the claim of the title in the areas of algebra, theoretical computer science, and theoretical physics. In algebra, we will consider the random graph and Ulm's theorem for countable abelian p-groups. For theoretical computer science, we will give a probabilistic construction of Scott domains and show that with probability 1 our construction produces a universal homogeneous domain. Finally, we consider causal sets which have been used as basic models for discrete space-time in quantum gravity.