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Prime models of finite computable dimension

  • Pavel Semukhin (a1)

Abstract

We study the following open question in computable model theory: does there exist a structure of computable dimension two which is the prime model of its first-order theory? We construct an example of such a structure by coding a certain family of c.e. sets with exactly two one-to-one computable enumerations into a directed graph. We also show that there are examples of such structures in the classes of undirected graphs, partial orders, lattices, and integral domains.

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Prime models of finite computable dimension

  • Pavel Semukhin (a1)

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