A topology generated by eventually different functions
A T-partial order obtained from T-norms
A partial order on a bounded lattice is called t-order if it is defined by means of the t-norm on . It is obtained that for a t-norm on a bounded lattice the relation iff for some is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of and a complete lattice on the subset of all elements of which are the supremum of a subset of atoms.
A tree axiom.
A tree -base for without cofinal branches
We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree -base for with no branches yet of height . We establish that this is also possible for using a natural modification of Mathias forcing.
A type of βN with relative types
A universal function for continuous functions
A universal null graph whose domain has positive measure
A weakening of the axiom of choice for the standard binary tree.
A weakening of , with applications to topology
A well ordering of the Cartesian product of two ordinals
Abelian group extensions and the axiom of constructibility.
About An Equivalent Of The Continuum Hypothesis
About the equivalence of nullnorms on bounded lattice
In this paper, an equivalence on the class of nullnorms on a bounded lattice based on the equality of the orders induced by nullnorms is introduced. The set of all incomparable elements w.r.t. the order induced by nullnorms is investigated. Finally, the recently posed open problems have been solved.
Absolute Indiscernibles and Standard Models of ZFC
Absolute points in
Abzählbarkeit und Wohlordenbarkeit
AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology
We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.
Accumulation functions on the ordinals
Addendum to “On Meager Additive and Null Additive Sets in the Cantor space and in ℝ” (Bull. Polish Acad. Sci. Math. 57 (2009), 91-99)
We prove in ZFC that there is a set and a surjective function H: A → ⟨0,1⟩ such that for every null additive set X ⊆ ⟨0,1), is null additive in . This settles in the affirmative a question of T. Bartoszyński.
Adding a lot of Cohen reals by adding a few. II
We study pairs (V, V₁), V ⊆ V₁, of models of ZFC such that adding κ-many Cohen reals over V₁ adds λ-many Cohen reals over V for some λ > κ.