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We prove the existence of a fixed point of non-expanding fuzzy multifunctions in $α$ -fuzzy preordered sets. Furthermore, we establish the existence of least and minimal fixed points of non-expanding fuzzy multifunctions in $α$ -fuzzy ordered sets.

Fixed points with respect to the L-slice homomorphism $σ_{a}$

K.S. Sabna, N.R. Mangalambal (2019)

Archivum Mathematicum

Given a locale $L$ and a join semilattice $J$ with bottom element $0_{J}$ , a new concept $(σ, J)$ called $L$ -slice is defined,where $σ$ is as an action of the locale $L$ on the join semilattice $J$ . The $L$ -slice $(σ, J)$ adopts topological properties of the locale $L$ through the action $σ$ . It is shown that for each $a \in L$ , $σ_{a}$ is an interior operator on $(σ, J)$ .The collection $M = {σ_{a}; a \in L}$ is a Priestly space and a subslice of $L$ - $Hom (J, J)$ . If the locale $L$ is spatial we establish an isomorphism between the $L$ -slices $(σ, L)$ and $(δ, M)$ . We have shown that the fixed set of $σ_{a}$ ,...

Fixpoint alternation : arithmetic, transition systems, and the binary tree

J. C. Bradfield (1999)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Fixpoint alternation: arithmetic, transition systems, and the binary tree

J. C. Bradfield (2010)

RAIRO - Theoretical Informatics and Applications

We provide an elementary proof of the fixpoint alternation hierarchy in arithmetic, which in turn allows us to simplify the proof of the modal mu-calculus alternation hierarchy. We further show that the alternation hierarchy on the binary tree is strict, resolving a problem of Niwiński.

Fixpoints, games and the difference hierarchy

Julian C. Bradfield (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 $Σ_{2}^{0}$ . 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

Julian C. Bradfield (2010)

RAIRO - Theoretical Informatics and Applications

F-limit points in dynamical systems defined on the interval

Piotr Szuca (2013)

Open Mathematics

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

Julius Barbanel (1989)

Fundamenta Mathematicae

Flipping properties and supercompact cardinals

Carlos Di Prasco, William Zwicker (1980)

Fundamenta Mathematicae

Folding theory applied to BL-algebras

Young Jun, Jung Ko (2004)

Open Mathematics

The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.

Foldness of Commutative Ideals in BCK-algebras

Celestin Lele, Salissou Moutari (2006)

Discussiones Mathematicae - General Algebra and Applications

This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.

Fonctions Généralisées et Analyse Non Standard.

Antoine Delcroix (1997)

Monatshefte für Mathematik

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