Fixed points of fuzzy monotone multifunctions
Under suitable conditions we prove the existence of fixed points of fuzzy monotone multifunctions.
Fixed Points Of Monotone Multifunctions In Partially Ordered Sets
Fixed points theorems for -fuzzy monotone maps.
Fixed points theorems of non-expanding fuzzy multifunctions
We prove the existence of a fixed point of non-expanding fuzzy multifunctions in -fuzzy preordered sets. Furthermore, we establish the existence of least and minimal fixed points of non-expanding fuzzy multifunctions in -fuzzy ordered sets.
Fixpoints, games and the difference hierarchy
Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over . This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.
Fixpoints, games and the difference hierarchy
Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over . This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.
F-limit points in dynamical systems defined on the interval
Given a free ultrafilter p on ℕ we say that x ∈ [0, 1] is the p-limit point of a sequence (x n)n∈ℕ ⊂ [0, 1] (in symbols, x = p -limn∈ℕ x n) if for every neighbourhood V of x, {n ∈ ℕ: x n ∈ V} ∈ p. For a function f: [0, 1] → [0, 1] the function f p: [0, 1] → [0, 1] is defined by f p(x) = p -limn∈ℕ f n(x) for each x ∈ [0, 1]. This map is rarely continuous. In this note we study properties which are equivalent to the continuity of f p. For a filter F we also define the ω F-limit set of f at x. We consider...
Flipping properties and huge cardinals
Flipping properties and supercompact cardinals
Forcing countable networks for spaces satisfying
We show that all finite powers of a Hausdorff space do not contain uncountable weakly separated subspaces iff there is a c.c.c poset such that in is a countable union of -dimensional subspaces of countable weight. We also show that this...
Forcing for hL and hd
The present paper addresses the problem of attainment of the supremums in various equivalent definitions of the hereditary density hd and hereditary Lindelöf degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk [13, Problems 50, 54], showing consistency of different attainment behaviour and proving that (for the variants considered) this is the best result we can expect.
Forcing in a general setting
Forcing in the alternative set theory. I
The technique of forcing is developed for the alternative set theory (AST) and similar weak theories, where it can be used to prove some new independence results. There are also introduced some new extensions of AST.
Forcing in the alternative set theory. II
By the technique of forcing, some new independence results are proved for the alternative set theory (AST) and similar weak theories: The scheme of choice is independent both of AST and of second order arithmetic, axiom of constructibility is independent of AST plus schemes of choice.
Forcing indestructible extensions of almost disjoint families
Forcing tightness in products of fans
We prove two theorems that characterize tightness in certain products of fans in terms of families of integer-valued functions. We also define several notions of forcing that allow us to manipulate the structure of the set of functions from some cardinal θ to ω, and hence, the tightness of these products. These results give new constructions of first countable <θ-cwH spaces that are not ≤θ-cwH.
Forcing when there are large cardinals: An introduction
Forcing with ideals generated by closed sets
Consider the poset where is an arbitrary -ideal -generated by a projective collection of closed sets. Then the extension is given by a single real of an almost minimal degree: every real is Cohen-generic over or .
Forcing with proper classes
Forcing with propositional Lindenbaum algebras.