Endofunctors of set and cardinalities
Endomorphic cuts and tails
Endomorphic universes and their standard extensions
Ensembles analytiques, théorèmes de séparation et applications
Entropy of -sums and -products of - fuzzy numbers
In the paper the entropy of – fuzzy numbers is studied. It is shown that for a given norm function, the computation of the entropy of – fuzzy numbers reduces to using a simple formula which depends only on the spreads and shape functions of incoming numbers. In detail the entropy of –sums and –products of – fuzzy numbers is investigated. It is shown that the resulting entropy can be computed only by means of the entropy of incoming fuzzy numbers or by means of their parameters without the...
Entscheidungsprobleme der Theorie zweier Äquivalenzrelationen mit beschränkter Zahl vоn Elementen in den Klassen
Épistémologie du transfini
Equimorphism invariants for scattered linear orderings
Two linear orderings are equimorphic if they can be embedded in each other. We define invariants for scattered linear orderings which classify them up to equimorphism. Essentially, these invariants are finite sequences of finite trees with ordinal labels. Also, for each ordinal α, we explicitly describe the finite set of minimal scattered equimorphism types of Hausdorff rank α. We compute the invariants of each of these minimal types..
Equivalence class in the set of fuzzy numbers and its application in decision-making problems.
Equivalence relations induced by some locally compact groups of homeomorphisms of
Let T be a locally finite rooted tree and B(T) be the boundary space of T. We study locally compact subgroups of the group TH(B(T)) = ⟨Iso(T),V⟩ generated by the group Iso(T) of all isometries of B(T) and the group V of Richard Thompson. We describe orbit equivalence relations arising from actions of these groups on B(T).
Equivalent fuzzy sets
Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Relationship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.
Equivariant measurable liftings
We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Möbius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semisimple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to -cocycles for characteristic classes.
Errata to "Lindelöf indestructibility, topological games and selection principles" (Fund. Math. 210 (2010), 1-46)
In [Fund. Math. 210 (2010), 1-46] we claimed the truth of two statements, one now known to be false and a second lacking a proof. In this "Errata" we report these matters in the interest of setting the record straight on the status of these claims.
Errata to the paper "Models of second order arithmetic with definable Skolem functions", Fundamenta Mathematicae 75 (1972), pp. 223-234
Erratum to "Fields of surreal numbers and exponentiation" (Fund. Math. 167 (2001), 173-188)
Erratum to the paper "The Axion of Choice, the Löwenheim–Skolem Theorem and Borel models" (Fund. Math. 137 (1991), 53-58)
Erweiterte Fassung eines von Clebsch aufgestellten Uebertragungsprincips und deren Anwendung
Essentially Rigid Floppy Subgroups of the Baer-Specker Group.
Estensioni contraddittorie della teoria Ampia
Dopo una breve presentazione della teoria , una teoria non riduzionista ed autoreferenziale dei fondamenti della matematica proposta da Clavelli, De Giorgi, Forti e Tortorelli nel 1987, si mostra l'inconsistenza di estensioni della teoria ottenute aggiungendo forti assiomi su relazioni e operazioni (ad es. assiomi che danno la composizione di operazioni, la congiunzione di relazioni, ecc.) e/o assiomi che forniscono qualche relazione "combinatoria".
Evaluating many valued modus ponens
This paper deals with many valued case of modus ponens. Cases with implicative and with clausal rules are studied. Many valued modus ponens via discrete connectives is studied with implicative rules as well as with clausal rules. Some properties of discrete modus ponens operator are given.