This is an abstract and references for a talk to be given at a Dynamical Systems Workshop at the Pennsylvania State University, Department of Mathematics, October 18-21, 2007.
We apply some fundamental concepts and results from mathematical logic in order to obtain an apparently new counterexample in symbolic dynamics. Two sets and are said to be strongly equivalent if there exist partial recursive functionals from into and vice versa. The strong degree of is the equivalence class of under strong equivalence. There is an extensive recursion-theoretic literature on the lattice of strong degrees of nonempty subsets of the Cantor space. This lattice is known as . We prove that consists precisely of the strong degrees of 2-dimensional subshifts of finite type. We use this result to obtain an infinite collection of 2-dimensional subshifts of finite type which are, in a certain sense, mutually incompatible.
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