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The study of the L-fuzzy concept lattice.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1994)

Mathware and Soft Computing

The L-Fuzzy concept theory that we have developed sets up classifications from the objects and attributes of a context through L-Fuzzy relations. This theory generalizes the formal concept theory of R. Wille. In this paper we begin with the L-Fuzzy concept definition that generalizes the definitions of the formal concept theory, and we study the lattice structure of the L-Fuzzy concept set, giving a constructive method for calculating this lattice. At the end, we apply this constructive method to...

The study on semicopula based implications

Zuming Peng (2020)

Kybernetika

Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula...

The sup = max problem for the extent and the Lindelöf degree of generalized metric spaces, II

Yasushi Hirata (2015)

Commentationes Mathematicae Universitatis Carolinae

In [The sup = max problem for the extent of generalized metric spaces, Comment. Math. Univ. Carolin. The special issue devoted to Čech 54 (2013), no. 2, 245–257], the author and Yajima discussed the sup = max problem for the extent and the Lindelöf degree of generalized metric spaces: (strict) p -spaces, (strong) Σ -spaces and semi-stratifiable spaces. In this paper, the sup = max problem for the Lindelöf degree of spaces having G δ -diagonals and for the extent of spaces having point-countable bases...

The sup = max problem for the extent of generalized metric spaces

Yasushi Hirata, Yukinobu Yajima (2013)

Commentationes Mathematicae Universitatis Carolinae

It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces.

The theory of definitions in the polish logical literature

Jan Gregorowicz (1991)

Mathématiques et Sciences Humaines

Analysis of some answers to the following questions : is there a generic notion of definition ? What is the difference between “analytic definition” and “synthetic definition” ? What is a good definition ?

The theory of dual groups

A. Mekler, G. Schlitt (1994)

Fundamenta Mathematicae

We study the L ∞ , w -theory of sequences of dual groups and give a complete classification of the L ∞ , w -elementary classes by finding simple invariants for them. We show that nonstandard models exist.

The tree property at both ℵ ω + 1 and ℵ ω + 2

Laura Fontanella, Sy David Friedman (2015)

Fundamenta Mathematicae

We force from large cardinals a model of ZFC in which ℵ ω + 1 and ℵ ω + 2 both have the tree property. We also prove that if we strengthen the large cardinal assumptions, then in the final model ℵ ω + 2 even satisfies the super tree property.

The tree property at the double successor of a measurable cardinal κ with 2 κ large

Sy-David Friedman, Ajdin Halilović (2013)

Fundamenta Mathematicae

Assuming the existence of a λ⁺-hypermeasurable cardinal κ, where λ is the first weakly compact cardinal above κ, we prove that, in some forcing extension, κ is still measurable, κ⁺⁺ has the tree property and 2 κ = κ ⁺ ⁺ ⁺ . If the assumption is strengthened to the existence of a θ -hypermeasurable cardinal (for an arbitrary cardinal θ > λ of cofinality greater than κ) then the proof can be generalized to get 2 κ = θ .

The Tree Property at ω₂ and Bounded Forcing Axioms

Sy-David Friedman, Víctor Torres-Pérez (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that the Tree Property at ω₂ together with BPFA is equiconsistent with the existence of a weakly compact reflecting cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for ω₂ together with BPFA is equiconsistent with the existence of a reflecting Mahlo cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a Mahlo cardinal....

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