Nonreflecting stationary subsets of
We explore the possibility of forcing nonreflecting stationary sets of . We also present a generalization of Kanamori’s weakly normal filters, which induces stationary reflection.
Non-separable Banach spaces with non-meager Hamel basis
We show that an infinite-dimensional complete linear space X has: ∙ a dense hereditarily Baire Hamel basis if |X| ≤ ⁺; ∙ a dense non-meager Hamel basis if for some cardinal κ.
Nonstandard models of arithmetic as an alternative basis for continuum considerations
Normal numbers and subsets of N with given densities
For X ⊆ [0,1], let denote the collection of subsets of ℕ whose densities lie in X. Given the exact location of X in the Borel or difference hierarchy, we exhibit the exact location of . For α ≥ 3, X is properly iff is properly . We also show that for every nonempty set X ⊆[0,1], is -hard. For each nonempty set X ⊆ [0,1], in particular for X = x, is -complete. For each n ≥ 2, the collection of real numbers that are normal or simply normal to base n is -complete. Moreover, , the...
Normal numbers and the Borel hierarchy
We show that the set of absolutely normal numbers is Π⁰₃-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is Π⁰₃-complete in the effective Borel hierarchy.
Normal restrictions of the noncofinal ideal on
We discuss the problem of whether there exists a restriction of the noncofinal ideal on that is normal.
Normality and Martin's axiom
Norms on possibilities. II: More ccc ideals on .
Note on a theorem of J. Baumgartner
Note on compatible binary relations on algebras
Note on connections of the point of continuity property and Kuratowski problem on function having the Baire property
Note on "construction of uninorms on bounded lattices"
In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.
Note sur la théorie des ensembles
Notes on lattice congruences
Notes on locally internal uninorm on bounded lattices
In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice . We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice , and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm.
Notes on revealed classes
Notions élémentaires de théorie descriptive effective
Novak's result by Henkin's method
Nowhere dense subsets and Booth's Lemma
The following statement is proved to be independent from : Let be a Tychonoff space with and . Then a union of less than of nowhere dense subsets of is a union of not greater than of nowhere dense subsets.