1,720,969 research outputs found
Il ruolo dell'infinito nel primo libro della Scienza della Logica di Georg Friedrich Hegel
No full textAn extension to R^k of a result by Fekete and Meijer
No full textGiven a finite configuration of points A in R k endowed with the Manhattan distance, we prove that the ratio of the sum of the distances from a centroid of A over the sum of the distances from the Steiner center of A is bounded by 1 + (k - 1) k; further, this bound can be attained. This fact extends to an arbitrary finite dimension k ≥ 2 a result proved by Fekete and Meijer for k ∈ {2, 3}
Applications of formative processes to the decision problem in set theory
No full textAs part of a project aimed at the implementation of a proof-checker based on the set-theoretic formalism, the decision problem in set theory has been studied very intensively, starting in the late seventies.
Several results have been produced in the first decade of research, giving rise to the novel field of computable set theory. At that point, it already was clear that to face the tremendous amount of technicalities involved in the combination of smaller decidable fragments into larger ones, new techniques were in order.
Such techniques have recently emerged, by a careful analysis of the formation process of disjoint families of sets. This has led to the characterization of suitable decidable conditions for the satisfiability of set-theoretic formulae belonging to specific collections.
In this paper we give an elementary introduction to the formative process technique and discuss some open problems
Formative processes with applications to the decision problem in set theory: II. Powerset and singleton operators, finiteness predicate
No full textIn this paper we solve the satisfiability problem for the quantifier-free fragment of set theory MLSSPF involving in addition to the basic Boolean set operators of union, intersection, and difference, also the powerset and singleton operators, and a finiteness predicate.
The more restricted fragment obtained by dropping the finiteness predicate has been shown to have a solvable satisfiability problem in a previous paper, by establishing for it a small model property.
We exploit the latter decision result for dealing also with the finiteness predicate (and therefore with the infiniteness predicate too) and prove a small witness-model property for MLSSPF, asserting that any model for a satisfiable formula Phi with m distinct variables of the fragment of our interest admits a finite representation bounded by c(m), where c is a suitable computable function. Since such candidate representations are finitely many, their number does not exceed a known bound, and it can be recognized algorithmically whether they indeed represent a(n infinite) model for the input formula, the decidability of the satisfiability problem for MLSSPF follows
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