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\(S\)-approximation: a new approach to algebraic approximation. (English) Zbl 1294.03033

Summary: We intend to study a new class of algebraic approximations, called \(S\)-approximations, and their properties. We have shown that \(S\)-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of \(S\)-approximations, called \(S_{\mathcal{M}}\)-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusion based. The paper concludes by studying some basic operations on \(S\)-approximations and counting the number of \(S\)-min functions.

MSC:

03E02 Partition relations
03E05 Other combinatorial set theory
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