Less Saturated Ideals
نویسندگان
چکیده
We prove the following: (1) If κ is weakly inaccessible then NSκ is not κ+-saturated. (2) If κ is weakly inaccessible and θ < κ is regular then NSθ κ is not κ +saturated. (3) If κ is singular then NS κ+ is not κ++-saturated. Combining this with previous results of Shelah, one obtains the following: (A) If κ > א1 then NSκ is not κ+-saturated. (B) If θ+ < κ then NSθ κ is not κ +-saturated.
منابع مشابه
Borel Fixed Initial Ideals of Prime Ideals in Dimension Two
We prove that if the initial ideal of a prime ideal is Borel-fixed and the dimension of the quotient ring is less than or equal to two, then given any non-minimal associated prime ideal of the initial ideal it contains another associated prime ideal of dimension one larger. Let R = k[x1, x2, . . . , xr] be a polynomial ring over a field. We will say that an ideal I ⊆ R has the saturated chain p...
متن کاملar X iv : m at h / 95 03 20 3 v 1 [ m at h . L O ] 1 M ar 1 99 5 LESS SATURATED IDEALS by Moti
We are proving the following: (1) If κ is a weakly inaccessible then NSκ is not κ -saturated. (2) If κ is a weakly inaccessible and θ < κ is regular then NS κ is not κ saturated. (3) If κ is singular then NS κ+ is not κ-saturated. Combining this with previous results of Shelah, one obtains the following: (A) If κ > א1 then NSκ is not κ -saturated. (B) If θ < κ then NS κ is not κ -saturated.
متن کاملSaturated ideals obtained via restricted iterated collapse of huge cardinals
A uniform method to define a (restricted iterated) forcing notion to collapse a huge cardinal to a small one to obtain models with various types of highly saturated ideals over small cardinals is presented. The method is discussed in great technical details in the first chapter, while in the second chapter the application of the method is shown on three different models: Model I with an א1-comp...
متن کاملThe Intergenerational Comparison of Marriage and Childbearing Ideals with Emphasis on Background Characteristics in Sanandaj District
The aim of this study is to investigate and compare marriage and childbearing ideals between two generations i.e. mothers and their offspring in Sanandaj district. The research data has been obtained from Sanandaj's Fertility Ideals and Behaviors Survey in 2014. A sample of 420 people was drawn from the available data, containing 210 mothers and 210 single offsprings (107 boys and 103 girls). T...
متن کاملA degree bound for the Graver basis of non-saturated lattices
Let $L$ be a lattice in $ZZ^n$ of dimension $m$. We prove that there exist integer constants $D$ and $M$ which are basis-independent such that the total degree of any Graver element of $L$ is not greater than $m(n-m+1)MD$. The case $M=1$ occurs precisely when $L$ is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. As a corollary, we show t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997