The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1 n n ∑ i=1 f(sφi(t)) (s, t ∈ S), where S is a semigroup and where φ1, . . . , φn : S → S are pairwise distinct automorphisms of S such that the set {φ1, . . . , φn} is a group equipped with the composition as the group operation. The main results state that if f satisfies a stabili...

Vaught’s Conjecture states that if Σ is a complete first order theory in a countable language such that Σ has uncountably many pairwise non-isomorphic countably infinite models, then Σ has 2א0 many pairwise non-isomorphic countably infinite models. Continuing investigations initiated in [17], we apply methods of algebraic logic to study some variants of Vaught’s conjecture. More concretely, let...

For a set M, fin(M) denotes the of all finite subsets M2 Cartesian product M×M, [M]2 2-element and seq1-1(M) sequences without repetition which can be formed with elements M. Furthermore, for S, let |S| denote cardinality S. Under assumption that four cardinalities |[M]2|, |M2|, |fin(M)|, |seq1-1(M)| are pairwise distinct comparable in ZF, there six possible linear orderings between these cardi...

For a countable, weakly minimal theory T , we show that the SchröderBernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to each of the following: 1. For any U -rank-1 type q ∈ S(acl(∅)) and any automorphism f of the monster model C, there is some n < ω such that f(q) is not almost orthogonal to q ⊗ f(q)⊗ . . .⊗ fn−1(q); 2. T has no infinite collection of ...

Pairwise comparison data are used in various contexts including the generation of weight vectors for multiple criteria decision making problems. If this data is not sufficiently consistent, then the resulting weight vector cannot be considered to be a reliable reflection of the evaluator s opinion. Hence, it is necessary to measure its level of inconsistency. Different approaches have been prop...

In [K–K–S] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows to construct for every κ regular uncountable cardinal, 2...

“Strategy-proofness” is one of the axioms that are most frequently used in the recent literature on social choice theory. It requires that by misrepresenting his preferences, no agent can manipulate the outcome of the social choice rule in his favor. The stronger requirement of “group strategy-proofness” is also often employed to obtain clear characterization results of social choice rules. Gro...

There is significant interest in inferring the structure of subcellular networks of interaction. Here we consider supervised interactive network inference in which a reference set of known network links and nonlinks is used to train a classifier for predicting new links. Many types of data are relevant to inferring functional links between genes, motivating the use of data integration. We use p...

In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+ 1)-sets violating this condition and still implying the considered Hamiltonian property. In this...

Short note: This is a supplementary text for the manuscript with the same title. The additions are the parts that handle stability under randomizations, pairwise p-value comparison of GSZ with other tested scoring functions, the most of the materials and methods, and derivation of E(S|N) and D(S|N) required for the derivation of the GSZ-score. This text represent five major findings: (a) Stabil...