Topic
Recursively enumerable language
About: Recursively enumerable language is a research topic. Over the lifetime, 1508 publications have been published within this topic receiving 32382 citations.
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TL;DR: The construction of a general-purpose defeasible reasoner that is complete for first-order logic and provably adequate for the argument-based conception of defeasibles reasoning that I have developed elsewhere is described.
312 citations
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TL;DR: The main theorem of as discussed by the authors states that a finitely generated group can be embedded in a finite presented group if and only if it has a recursively enumerable set of defining relations.
Abstract: The main theorem of this paper states that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. It follows that every countable A belian group, and every countable locally finite group can be so embedded; and that there exists a finitely presented group which simultaneously embeds all finitely presented groups. A nother corollary of the theorem is the known fact that there exist finitely presented groups with recursively insoluble word problem . A by-product of the proof is a genetic characterization of the recursively enumerable subsets of a suitable effectively enumerable set.
304 citations
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259 citations
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TL;DR: In this paper, the authors considered a set of non-logical axioms of the classical functional calculus with the assumption that the set A is recursive, or at least recursively enumerable.
Abstract: The theories considered here are based on the classical functional calculus (possibly of higher order) together with a set A of non-logical axioms; they are also assumed to contain classical first-order number theory. In foundational investigations it is customary to further restrict attention to the case that A is recursive, or at least recursively enumerable (an equivalent restriction, by [1]). For such axiomatic theories we have the well-known incompleteness phenomena discovered by Godei [6]. Quite far removed from such theories are those based on non-constructive sets of axioms, for example the set of all true sentences of first-order number theory. According to Tarski's theorem, there is not even an arithmetically definable set of axioms A which will give the same result (cf. [18] for exposition).
246 citations
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TL;DR: Several representations of the recursively enumerable (r.e.) sets are presented and it is shown that this automata theoretic representation cannot be strengthened by restricting the acceptors to be deterministic multitape, nondeterministic one-tape, or nondetergetic multicounter acceptors.
241 citations