Embedding Cohen algebras using pcf theory
Using a theorem from pcf theory, we show that for any singular cardinal ν, the product of the Cohen forcing notions on κ, κ < ν, adds a generic for the Cohen forcing notion on .
Embedding of Boolean algebras in Ρ(ω)/fin
Embedding orders into the cardinals with
Jech proved that every partially ordered set can be embedded into the cardinals of some model of ZF. We extend this result to show that every partially ordered set can be embedded into the cardinals of some model of for any regular κ. We use this theorem to show that for all κ, the assumption of does not entail that there are no decreasing chains of cardinals. We also show how to extend the result to and embed into the cardinals a proper class which is definable over the ground model. We use...
Embedding partially ordered sets into
We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).
Embeddings into 𝓟(ℕ)/fin and extension of automorphisms
Given a Boolean algebra 𝔹 and an embedding e:𝔹 → 𝓟(ℕ)/fin we consider the possibility of extending each or some automorphism of 𝔹 to the whole 𝓟(ℕ)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.
Emploi des filtres sur N dans l'étude descriptive des fonctions
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