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11.
Characteristic, C-characteristic and positive cones in hyperfields
Dawid Edmund Kędzierski, Alessandro Linzi, Hanna Stojałowska, 2023, original scientific article

Abstract: We study the notions of positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We show how these interact in order to produce interesting results in the theory of hyperfields. For instance, we give a criterion for deciding whether certain hyperfields cannot be obtained via Krasner's quotient construction. We prove that any positive integer (larger than 1) can be realized as the characteristic of some infinite hyperfield and an analogous result for C-characteristic. Finally, we study the (directed) graph associated to the strict partial order induced by a positive cone in a hyperfield in various examples.
Keywords: hyperfield, order, characteristic, positive cone
Published in RUNG: 13.02.2023; Views: 924; Downloads: 3
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12.
Dependence relations and grade fuzzy set
Alessandro Linzi, Irina Elena Cristea, 2023, original scientific article

Abstract: With the aim of developing the recent theory of dependence relations, we elaborate a procedure to measure the strength of the influence of an element on another with respect to a given dependence relation on a finite set. We call this measure the degree of influence. Its definition is based on a partial hyperoperation and a directed graph which we associate with any dependence relation. We compute the degree of influence in various examples and prove some general properties. Among these properties, we find symmetries that have the potential to be applied in the realization of effective algorithms for the computations.
Keywords: dependence relation, degree of influence, grade fuzzy set, hypercompositional structure, hyperoperation
Published in RUNG: 23.01.2023; Views: 1234; Downloads: 3
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13.
Algebraic hyperstructures in the model theory of valued fields : PhD in mathematics
Alessandro Linzi, 2022, doctoral dissertation

Keywords: hyperfield, valued field, algebra, model theory, quantifier elimination
Published in RUNG: 27.10.2022; Views: 1291; Downloads: 80
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14.
Krasner hyperfields and the model theory of valued fields
Alessandro Linzi, unpublished conference contribution

Keywords: hyperfield, valued field, model theory, quantifier elimination, valuation, subhyperfield
Published in RUNG: 10.10.2022; Views: 966; Downloads: 0
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15.
Structures for relative quantifier elimination in valued fields : Algebraic hyperstructures in the model theory of valued fields
Alessandro Linzi, invited lecture at foreign university

Keywords: model theory, quantifier elimination, valued field, hyperfield
Published in RUNG: 10.10.2022; Views: 1002; Downloads: 0
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16.
Structures for quantifier elimination in valued fields
Alessandro Linzi, unpublished conference contribution

Keywords: quantifier elimination, model theory, valued field, hyperfield
Published in RUNG: 10.10.2022; Views: 915; Downloads: 0
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17.
Krasner hyperfields and the model theory of valued fields
Alessandro Linzi, unpublished conference contribution

Keywords: hyperfield, valued field, model theory, quantifier elimination
Published in RUNG: 07.10.2022; Views: 1097; Downloads: 0
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18.
Krasner hyperfields and the model theory of valued fields
Alessandro Linzi, published scientific conference contribution abstract

Keywords: hyperfield, valued field, model theory, quantifier elimination
Published in RUNG: 07.10.2022; Views: 1064; Downloads: 0
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19.
The Christi-Kirk Fixed Point Theorem and equivalent principles : A viewpoint from the theory of ballspaces
Alessandro Linzi, unpublished invited conference lecture

Keywords: ball space, fixed point theorem, metric space, Caristi-Kirk, Oettli-Thera
Published in RUNG: 07.10.2022; Views: 848; Downloads: 0
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20.
Structures for relative quantifier elimination in valued fields
Alessandro Linzi, 2022, published scientific conference contribution abstract

Keywords: quantifier elimination, model theory, valued field
Published in RUNG: 07.10.2022; Views: 1098; Downloads: 5
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