Stationary reflection and ideals

1994 ◽  
Vol 59 (1) ◽  
pp. 182-184
Author(s):  
Shu-Guo Zhang
Keyword(s):  
Normal Ideal ◽  
Stationary Reflection

AbstractIn this paper we show that if there is a weakly normal ideal on κ then for each fails. This greatly improves a theorem of C. A. Johnson.

On BF-algebras

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
Andrzej Walendziak
Keyword(s):  
Normal Ideal

AbstractIn this paper we introduce the notion of BF-algebras, which is a generalization of B-algebras. We also introduce the notions of an ideal and a normal ideal in BF-algebras. We investigate the properties and characterizations of them.

scholarly journals Stationary reflection and level by level equivalence

2009 ◽  
Vol 115 (1) ◽  
pp. 113-128
Author(s):  
Arthur W. Apter
Keyword(s):  
Stationary Reflection

scholarly journals Indestructibility and stationary reflection

2009 ◽  
Vol 55 (3) ◽  
pp. 228-236 ◽  
Author(s):  
Arthur W. Apter
Keyword(s):  
Stationary Reflection

Hysteresis effect in stationary reflection of shock waves

1995 ◽  
Vol 7 (4) ◽  
pp. 685-687 ◽  
Author(s):  
M. S. Ivanov ◽  
S. F. Gimelshein ◽  
A. E. Beylich
Keyword(s):  
Shock Waves ◽  
Hysteresis Effect ◽  
Stationary Reflection

scholarly journals IDEAL PROJECTIONS AND FORCING PROJECTIONS

2014 ◽  
Vol 79 (4) ◽  
pp. 1247-1285 ◽  
Author(s):  
SEAN COX ◽  
MARTIN ZEMAN
Keyword(s):  
Set Theory ◽  
Negative Answer ◽  
Large Cardinals ◽  
Normal Ideal ◽  
List Type ◽  
Type Number ◽  
Inner Model ◽  
Image Position ◽  
Open Question ◽  
Woodin Cardinal

AbstractIt is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman–Magidor–Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove:(1)If${\cal I}$is a normal ideal on$\omega _2 $which satisfiesstationary antichain catching, then there is an inner model with a Woodin cardinal;(2)For any$n \in \omega $, it is consistent relative to large cardinals that there is a normal ideal${\cal I}$on$\omega _n $which satisfiesprojective antichain catching, yet${\cal I}$is not saturated (or even strong). This provides a negative answer to Open Question number 13 from Foreman’s chapter in the Handbook of Set Theory ([7]).

scholarly journals Standard Ideals in BCL+ Algebras

2016 ◽  
Vol 8 (2) ◽  
pp. 37
Author(s):  
Yonghong Liu
Keyword(s):  
Proper Ideal ◽  
Normal Ideal ◽  
Normal Extension

We show some useful properties of these ideals that give various methods how to get ideals from them, and so our main aim is to study their properties. Here, we introduce these ideals i.e., the natural ideal, normal ideal, former ideal (and its doublet, latter ideal), proper ideal, normal extension ideal, normal uptake ideal. In particular, we introduce Boolean ideal and normal Boolean ideal to grasp the diversity of ideal for BCL+ algebras. As a means, we can define quotient BCL+ algebras only in terms of ideal, and we discuss its structure.

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