Cofinality of normal ideals onP κ(λ) II

2005 ◽  
Vol 150 (1) ◽  
pp. 253-283 ◽  
Author(s):  
Pierre Matet ◽  
Cédric Péan ◽  
Saharon Shelah
Keyword(s):  
Normal Ideals

Normal ideals in generalized almost distributive fuzzy lattices

2020 ◽  
Author(s):  
S. G. Karpagavalli ◽  
T. Sangeetha
Keyword(s):  
Normal Ideals

scholarly journals Cardinal preserving ideals

1999 ◽  
Vol 64 (4) ◽  
pp. 1527-1551 ◽  
Author(s):  
Moti Gitik ◽  
Saharon Shelah
Keyword(s):  
Consistency Strength ◽  
Normal Ideals

AbstractWe give some general criteria, when κ-complete forcing preserves largeness properties—like κ-presaturation of normal ideals on λ (even when they concentrate on small cofinalities). Then we quite accurately obtain the consistency strength “NSλ is αi-preserving”, for λ > α2.

scholarly journals (Fuzzy) Ideals of BN-Algebras

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Grzegorz Dymek ◽  
Andrzej Walendziak
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Ideal ◽  
One To One ◽  
Normal Ideals

The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained.

Iterated forcing and normal ideals onω 1

1987 ◽  
Vol 60 (3) ◽  
pp. 345-380 ◽  
Author(s):  
Saharon Shelah
Keyword(s):  
Iterated Forcing ◽  
Normal Ideals

scholarly journals Row ideals of certain normal ideals

2005 ◽  
Vol 201 (1-3) ◽  
pp. 240-249
Author(s):  
Mark R. Johnson
Keyword(s):  
Normal Ideals

Partition Relations for Strongly Normal Ideals on P()

2000 ◽  
Vol 46 (1) ◽  
pp. 87-103 ◽  
Author(s):  
Pierre Matet
Keyword(s):  
Partition Relations ◽  
Normal Ideals

Normal Ideals and Expected Reduction Numbers#

2005 ◽  
Vol 33 (10) ◽  
pp. 3787-3795 ◽  
Author(s):  
Mark R. Johnson ◽  
Susan E. Morey
Keyword(s):  
Normal Ideals

Large normal ideals concentrating on a fixed small cardinality

1996 ◽  
Vol 35 (5-6) ◽  
pp. 341-347 ◽  
Author(s):  
Saharon Shelah
Keyword(s):  
Small Cardinality ◽  
Normal Ideals

Combinatorics on large cardinals

1992 ◽  
Vol 57 (2) ◽  
pp. 617-643 ◽  
Author(s):  
Carlos H. Montenegro E.
Keyword(s):  
Regular Cardinal ◽  
Ordered Set ◽  
Large Cardinals ◽  
Large Cardinal ◽  
Combinatorial Properties ◽  
A Chain ◽  
Linearly Ordered Set ◽  
Normal Ideals ◽  
The Ideal

Our framework is ZFC, and we view cardinals as initial ordinals. Baumgartner ([Bal] and [Ba2]) studied properties of large cardinals by considering these properties as properties of normal ideals and not as properties of cardinals alone. In this paper we study these combinatorial properties by defining operations which take as input one or more ideals and give as output an ideal associated with a large cardinal property. We consider four operations T, P, S and C on ideals of a regular cardinal κ, and study the structure of the collection of subsets they give, and the relationships between them.The operation T is defined using combinatorial properties based on trees 〈X, <T〉 on subsets X ⊆ κ (where α <T β → α < β). Given an ideal I, consider the property *: “every tree on κ with every branching set in I has a branch of size κ” (where a branching set is a maximal set with the same set of <T-predecessors, and a chain is a maximal <T-linearly ordered set; for definitions see §2). Now consider the collection T(I) of all subsets of κ that do not satisfy * (see Definition 2.2 and the introduction to §5). The operation T provides us with the large cardinal property (whether κ ∈ T(I) or not) and it also provides us with the ideal associated with this large cardinal property (namely T(I)); in general, we obtain different notions depending on the ideal I.

scholarly journals Normal ideals of graded rings

2000 ◽  
Vol 28 (4) ◽  
pp. 1971-1977 ◽  
Author(s):  
Sara Faridi
Keyword(s):  
Graded Rings ◽  
Normal Ideals
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