Choice Functions on Posets

In the paper we study choice functions on posets satisfying the conditions of heredity and outcast. For every well-ordered sequence of elements of a poset, we define the corresponding ‘elementary’ choice function. Every such choice function satisfies the conditions of heredity and outcast. Inversely...

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Bibliographic Details
Published inOrder (Dordrecht) Vol. 40; no. 2; pp. 387 - 396
Main Author Danilov, I
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.07.2023
Springer Nature B.V
Subjects
Algebra
Discrete Mathematics
Heredity
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Set theory
Order ideal
Filter
Well order
Path independence
Stable contract
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Summary:In the paper we study choice functions on posets satisfying the conditions of heredity and outcast. For every well-ordered sequence of elements of a poset, we define the corresponding ‘elementary’ choice function. Every such choice function satisfies the conditions of heredity and outcast. Inversely, every choice function satisfying the conditions of heredity and outcast can be represented as a union of several elementary choice functions. This result generalizes the Aizerman-Malishevski theorem about the structure of path-independent choice functions.
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-022-09618-2