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Extensions of Witness Mappings

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Abstract

We deal with the problem of coexistence in interval effect algebras using the notion of a witness mapping. Suppose that we are given an interval effect algebra E, a coexistent subset S of E, a witness mapping β for S, and an element t ∈ E ∖ S. We study the question whether there is a witness mapping β t for S ∪ {t} such that β t is an extension of β. In the main result, we prove that such an extension exists if and only if there is a mapping e t from finite subsets of S to E satisfying certain conditions. The main result is then applied several times to prove claims of the type “If t has a such-and-such relationship to S and β, then β t exists”.

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Authors and Affiliations

  1. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak Technical University, Radlinského 11, Bratislava, 813 68, Slovak Republic

    Gejza Jenča

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  1. Gejza Jenča
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Correspondence to Gejza Jenča.

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This research is supported by grants VEGA G-1/0080/10,G-1/0297/11 of MŠ SR, Slovakia and by the Slovak Research and Development Agency under the contracts APVV-0071-06 and APVV-0073-10.

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Jenča, G. Extensions of Witness Mappings. Order 29, 533–544 (2012). https://doi.org/10.1007/s11083-011-9219-z

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  • DOI: https://doi.org/10.1007/s11083-011-9219-z

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