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Displaying 101 – 120 of 208

Relatively recursive expansions

C. Ash, J. Knight (1992)

Fundamenta Mathematicae

In this paper, we consider the following basic question. Let A be an L-structure and let ψ be an infinitary sentence in the language L∪R, where R is a new relation symbol. When is it the case that for every B ≅ A, there is a relation R such that (B,R) ⊨ ψ and $R \leq_{T} D (B)$ ? We succeed in giving necessary and sufficient conditions in the case where ψ is a “recursive” infinitary $Π_{2}$ sentence. (A recursive infinitary formula is an infinitary formula with recursive disjunctions and conjunctions.) We consider also...

Relatively recursive expansions II

C. Ash, J. Knight, Theodore Slaman (1993)

Fundamenta Mathematicae

In [AK], we asked when a recursive structure A and a sentence φ, with a new relation symbol, have the following property: for each ℬ≅ A there is a relation S such that S is recursive relative to ℬ and ℬ,S)⊨ φ. Here we consider several related properties, in which there is a uniform procedure for determining S from ℬ ≅A, or from ℬ,¯b)≅(A,ā), for some fixed sequence of parameters ā from A; or in which ℬ and S are required to be recursive. We investigate relationships between these properties, showing...

Relativization of cylindric algebras

Leon Henkin, Diane Resek (1975)

Fundamenta Mathematicae

Relativizations of the P = NP problem over the complex number field.

Rybalov, A.N. (2004)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

Relativnullen und reduzible Mengen bei Differenzen von Mengen ganzer Zahlen.

E. Härtter, G. Hofmeister, J. Zöllner (1978)

Journal für die reine und angewandte Mathematik

Relevance and redundancy in fuzzy classification systems.

Ana Del Amo, Daniel Gómez, Javier Montero, Gregory S. Biging (2001)

Mathware and Soft Computing

Fuzzy classification systems is defined in this paper as an aggregative model, in such a way that Ruspini classical definition of fuzzy partition appears as a particular case. Once a basic recursive model has been accepted, we then propose to analyze relevance and redundancy in order to allow the possibility of learning from previous experiences. All these concepts are applied to a real picture, showing that our approach allows to check quality of such a classification system.