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Switch to: References
Citations of:
Labelling systems and R.E. structures
Annals of Pure and Applied Logic 47 (2):99-119 (1990)
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Calhoun, W.C., Incomparable prime ideals of recursively enumerable degrees, Annals of Pure and Applied Logic 63 39–56. We show that there is a countably infinite antichain of prime ideals of recursively enumerable degrees. This solves a generalized form of Post's problem. |
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We re-express a previous general result in a way which seems easier to remember, using the terminology of infinite games. We show how this can be applied to construct recursive linear orderings, showing, for example, that if there is a ▵ 0 2β + 1 linear ordering of type τ, then there is a recursive ordering of type ω β · τ. |
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We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is${\rm{\Delta }}_\alpha ^0 $-complete for someα. To prove this, we extend Montalbán’sη-system framework to deal with limit ordinals in a more general way. We also show that, for any fixed computable structure, there is an ordinalαand a cone in the Turing degrees such that the exact complexity (...) |
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In [7] and [8], it is established that given any abstract countable structure S and a relation R on S, then as long as S has a recursive copy satisfying extra decidability conditions, R will be ∑0α on every recursive copy of S iff R is definable in S by a special type of infinitary formula, a ∑rα() formula. We generalize the typ e of constructions of these papers to produce conditions under which, given two disjoint relations R1 and R2 (...) |
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The degrees of unsolvability were introduced in the ground-breaking papers of Post [20] and Kleene and Post [7] as an attempt to measure theinformation contentof sets of natural numbers. Kleene and Post were interested in the relative complexity of decision problems arising naturally in mathematics; in particular, they wished to know when a solution to one decision problem contained the information necessary to solve a second decision problem. As decision problems can be coded by sets of natural numbers, this question (...) |
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We say that a theory [Formula: see text] satisfies arithmetic-is-recursive if any [Formula: see text]-computable model of [Formula: see text] has an [Formula: see text]-computable copy; that is, the models of [Formula: see text] satisfy a sort of jump inversion. We give an example of a theory satisfying arithmetic-is-recursive non-trivially and prove that the theories satisfying arithmetic-is-recursive on a cone are exactly those theories with countably many [Formula: see text]-back-and-forth types. |
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In this paper, we state a metatheorem for constructions involving coding. Using the metatheorem, we obtain results on coding a family of sets into a family of relations, or into a single relation. For a concrete example, we show that the set of limit points in a recursive ordering of type ω 2 can have arbitrary 2-REA degree. |
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Let be a model of a theory T. Depending on wether is decidable or recursive, and on whether T is strongly minimal or -minimal, we find conditions on which guarantee that every infinite independent subset of is not recursively enumerable. For each of the same four cases we also find conditions on which guarantee that every infinite independent subset of has Turing degree 0'. More generally, let be a recursive -structure, R a relation symbol not in , ψ a recursive (...) |
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