Partial orderings with the weak Freese-Nation property
نویسندگان
چکیده
منابع مشابه
Partial Orderings with the Weak Freese-Nation Property
A partial ordering P is said to have the weak Freese-Nation property (WFN) if there is a mapping f : P → [P ]0 such that, for any a, b ∈ P , if a ≤ b then there exists c ∈ f(a) ∩ f(b) such that a ≤ c ≤ b. In this note, we study the WFN and some of its generalizations. Some features of the class of Boolean algebras with the WFN seem to be quite sensitive to additional axioms of set theory: e.g.,...
متن کامل1 5 A ug 1 99 5 Partial orderings with the weak Freese - Nation property
A partial ordering P is said to have the weak Freese-Nation property (WFN) if there is a mapping f : P → [P ]0 such that, for any a, b ∈ P , if a ≤ b then there exists c ∈ f(a) ∩ f(b) such that a ≤ c ≤ b. In this note, we study the WFN and some of its generalizations. Some features of the class of Boolean algebras with the WFN seem to be quite sensitive to additional axioms of set theory: e.g.,...
متن کاملOn the weak Freese-Nation property of complete Boolean algebras
The following results are proved: (a) In a model obtained by adding א2 Cohen reals, there is always a c.c.c. complete Boolean algebra without the weak Freese-Nation property. (b) Modulo the consistency strength of a supercompact cardinal, the existence of a c.c.c. complete Boolean algebra without the weak Freese-Nation property is consistent with GCH. (c) If a weak form of 2μ and cof([μ] א0 ,⊆)...
متن کاملOn the weak Freese-Nation property of P(ω)
Continuing [6], [8] and [15], we study the consequences of the weak Freese-Nation property of (P(ω),⊆). Under this assumption, we prove that most of the known cardinal invariants including all of those appearing in Cichoń’s diagram take the same value as in the corresponding Cohen model. Using this principle we could also strengthen two results of W. Just about cardinal sequences of superatomic...
متن کامل3 M ay 1 99 6 More set - theory around the weak Freese - Nation property
For a regular κ, a partial ordering P is said to have the κ Freese-Nation property (the κ-FN for short) if there is a mapping (κ-FN mapping) f : P → [P ] such that for any p, q ∈ P if p ≤ q then there is r ∈ f(p) ∩ f(q) such that p ≤ r ≤ q. Freese and Nation [5] used the א0-FN in a characterization of projective lattices and asked if this property alone already characterizes the projectiveness....
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1996
ISSN: 0168-0072
DOI: 10.1016/0168-0072(95)00047-x