scholarly journals The new operations on complete ideals

2019 ◽  
Vol 17 (1) ◽  
pp. 415-422 ◽  
Author(s):  
Joanna Jureczko
Keyword(s):  
Complete Ideal ◽  
Precipitous Ideals

Abstract We introduce the notion of K-ideals associated with Kuratowski partitions. Using new operations on complete ideals we show connections between K-ideals and precipitous ideals and prove that every complete ideal can be represented by some K-ideal.

scholarly journals Distributive and related ideals in generic extensions

1987 ◽  
Vol 106 ◽  
pp. 91-100
Author(s):  
C. A. Johnson
Keyword(s):  
Quotient Algebra ◽  
Complete Ideal ◽  
Naturally Occurring ◽  
Uncountable Cardinal ◽  
Game Theoretic ◽  
Generic Extensions

Let κ: be a regular uncountable cardinal and I a κ-complete ideal on te. In [11] Kanai proved that the μ-distributivity of the quotient algebra P(κ)I is preserved under κ-C.C. μ-closed forcing. In this paper we extend Kanai’s result and also prove similar preservation results for other naturally occurring forms of distributivity. We also consider the preservation of two game theoretic properties of I and in particular, using a game theoretic equivalent of precipitousness we give a new proof of Kakuda’s theorem ([10]) that the precipitousness of I is preserved under κ-C.C. forcing.

Ideal balanced pairs

2020 ◽  
pp. 2150065
Author(s):  
Javad Asadollahi ◽  
Sara Hemat ◽  
Razieh Vahed
Keyword(s):  
Abelian Category ◽  
Derived Categories ◽  
Complete Ideal

In this paper, ideal balanced pairs in an abelian category will be introduced and studied. It is proved that every ideal balanced pair gives rise to a triangle equivalence of relative derived categories. We define complete ideal cotorsion triplets and investigate their relation with ideal balanced pairs.

Precipitous ideals

1980 ◽  
Vol 45 (1) ◽  
pp. 1-8 ◽  
Author(s):  
T. Jech ◽  
M. Magidor ◽  
W. Mitchell ◽  
K. Prikry
Keyword(s):  
Large Cardinals ◽  
Large Cardinal ◽  
Ground Model ◽  
Generic Set ◽  
Precipitous Ideal ◽  
Precipitous Ideals ◽  
The Ideal

The properties of small cardinals such as ℵ1 tend to be much more complex than those of large cardinals, so that properties of ℵ1 may often be better understood by viewing them as large cardinal properties. In this paper we show that the existence of a precipitous ideal on ℵ1 is essentially the same as measurability.If I is an ideal on P(κ) then R(I) is the notion of forcing whose conditions are sets x ∈ P(κ)/I, with x ≤ x′ if x ⊆ x′. Thus a set D R(I)-generic over the ground model V is an ultrafilter on P(κ) ⋂ V extending the filter dual to I. The ideal I is said to be precipitous if κ ⊨R(I)(Vκ/D is wellfounded).One example of a precipitous ideal is the ideal dual to a κ-complete ultrafilter U on κ. This example is trivial since the generic ultrafilter D is equal to U and is already in the ground model. A generic set may be viewed as one that can be worked with in the ground model even though it is not actually in the ground model, so we might expect that cardinals such as ℵ1 that cannot be measurable still might have precipitous ideals, and such ideals might correspond closely to measures.

scholarly journals The structure of precipitous ideals

1980 ◽  
Vol 106 (1) ◽  
pp. 47-52
Author(s):  
Stanley Wagon
Keyword(s):  
Precipitous Ideals

When Is a Complete Ideal in a Rational Surface Singularity a Multiplier Ideal?

2021 ◽  
pp. 145-151
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Víctor González-Alonso
Keyword(s):  
Rational Surface ◽  
Surface Singularity ◽  
Complete Ideal ◽  
Rational Surface Singularity ◽  
Multiplier Ideal

A MODEL WITH A PRECIPITOUS IDEAL, BUT NO NORMAL PRECIPITOUS IDEAL

2013 ◽  
Vol 13 (01) ◽  
pp. 1250008
Author(s):  
MOTI GITIK
Keyword(s):  
Measurable Cardinal ◽  
Precipitous Ideal ◽  
Precipitous Ideals

Starting with a measurable cardinal κ of the Mitchell order κ++ we construct a model with a precipitous ideal on ℵ1 but without normal precipitous ideals. This answers a question by T. Jech and K. Prikry. In the constructed model there are no Q-point precipitous filters on ℵ1, i. e. those isomorphic to extensions of Cubℵ1.

Complete ideal and n-ideal of B-algebra

2017 ◽  
Vol 11 ◽  
pp. 1705-1713
Author(s):  
Habeeb Kareem Abdullah ◽  
Arkan Ajeal Atshan
Keyword(s):  
Complete Ideal
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