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- W119870785 abstract "We consider the Turing degrees of prime models of complete decidable theories. In particular we show that every complete decidable atomic theory has a prime model whose elementary diagram is low. If we have a complete decidable atomic theory with all types of the theory computable, we show that for every degree d with 0 < d ≤ 0′, there is a prime model with elementary diagram of degree d. We say that a set X is prime bounding if for every complete decidable atomic theory T there is a prime model U of T decidable in X. In joint work with Denis Hirschfeldt, Julia Knight, and Robert Soare, we give the characterization that the prime bounding sets X ≤T ∅ ′ are exactly the sets which are not low2. Recent results of Alex Nabutovsky and Schmuel Weinberger in differential geometry have required the construction by Robert Soare of a certain sequence of computably enumerable sets. Weinberger later asked for a stronger sequence, which we construct. In addition, he introduced an ordering with geometric applications and asked for its computability theoretic properties, which we study." @default.
- W119870785 created "2016-06-24" @default.
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- W119870785 date "2003-01-01" @default.
- W119870785 modified "2023-09-26" @default.
- W119870785 title "Applications of computability theory to prime models and differential geometry" @default.
- W119870785 hasPublicationYear "2003" @default.
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