scholarly journals Partitioning a reflecting stationary set

2020 ◽  
Vol 148 (8) ◽  
pp. 3551-3565 ◽  
Author(s):  
Maxwell Levine ◽  
Assaf Rinot
Keyword(s):  
Stationary Set

On a topological construction of Juhasz and Shelah

1992 ◽  
Vol 57 (1) ◽  
pp. 166-171
Author(s):  
Dan Velleman
Keyword(s):  
Topological Space ◽  
Additional Structure ◽  
Homogeneous Set ◽  
Stationary Set ◽  
Topological Construction

In [2], Juhasz and Shelah use a forcing argument to show that it is consistent with GCH that there is a 0-dimensional T2 topological space X of cardinality ℵ3 such that every partition of the triples of X into countably many pieces has a nondiscrete (in the topology) homogeneous set. In this paper we will show how to construct such a space using a simplified (ω2, 1)-morass with certain additional structure added to it. The additional structure will be a slight strengthening of a built-in ◊ sequence, analogous to the strengthening of ordinary ◊k to ◊S for a stationary set S ⊆ k.Suppose 〈〈θα∣ ∝ ≤ ω2〉, 〈∝β∣α < β ≤ ω2〉〉 is a neat simplified (ω2, 1)-morass (see [3]). Let ℒ be a language with countably many symbols of all types, and suppose that for each α < ω2, α is an ℒ-structure with universe θα. The sequence 〈α∣α < ω2 is called a built-in ◊ sequence for the morass if for every ℒ-structure with universe ω3 there is some α < ω2 and some f ∈αω2 such that f(α) ≺ , where f(α) is the ℒ-structure isomorphic to α under the isomorphism f. We can strengthen this slightly by assuming that α is only defined for α ∈ S, for some stationary set S ⊆ ω2. We will then say that is a built-in ◊ sequence on levels in S if for every ℒ-structure with universe ω3 there is some α ∈ S and some f ∈ αω2 such that f(α) ≺ .

Increasing u2 by a stationary set preserving forcing

2009 ◽  
Vol 74 (1) ◽  
pp. 187-200
Author(s):  
Benjamin Claverie ◽  
Ralf Schindler
Keyword(s):  
Regular Cardinal ◽  
Nonstationary Ideal ◽  
Stationary Set ◽  
Precipitous Ideal ◽  
Countable Structure

AbstractWe show that if I is a precipitous ideal on ω1 and if θ > ω1 is a regular cardinal, then there is a forcing ℙ = ℙ(I, θ) which preserves the stationarity of all I-positive sets such that in Vℙ, ⟨Hθ; ∈, I⟩ is a generic iterate of a countable structure ⟨M; ∈, Ī⟩. This shows that if the nonstationary ideal on ω1 is precipitous and exists, then there is a stationary set preserving forcing which increases . Moreover, if Bounded Martin's Maximum holds and the nonstationary ideal on ω1 is precipitous, then .

scholarly journals Condition Absolute Stability Control System of Electromagnetoelastic Actuator for Communication Equipment

2020 ◽  
Vol 8 (1) ◽  
pp. 08-15 ◽  
Author(s):  
Sergey Mikhailovich Afonin
Keyword(s):  
Control System ◽  
Absolute Stability ◽  
Stability Control ◽  
Straight Line ◽  
Stability Control System ◽  
Stationary Set ◽  
The Absolute ◽  
Communication Equipment ◽  
Stable Control

We obtained the condition absolute stability on the derivative for the control system of electromagnetoelastic actuator for communication equipment. We applied the frequency methods for Lyapunov stable control system to calculate the condition absolute stability control system of electromagnetoelastic actuator. We used Yakubovich criterion absolute stability system with the condition on the derivative. The aim of this work is to determine the condition of the absolute stability on the derivative for the control system of electromagnetoelastic actuator. We received the stationary set of the control system of the hysteresis deformation of the electromagnetoelastic actuator. The stationary set is the segment of the straight line.

scholarly journals Stationary subspaces in ordered spaces

1989 ◽  
Vol 40 (3) ◽  
pp. 381-387
Author(s):  
Nobuyuki Kemoto
Keyword(s):  
Regular Cardinal ◽  
Closed Subspace ◽  
Stationary Set

In this paper, we shall characterise the B(k)-property in generalised ordered (GO) spaces as follows.For every uncountable regular cardinal K, every GO space has the B(K)-property if and only if it has no closed subspace which is homeomorphic to a stationary set in K (with the subspace topology in K).

scholarly journals Ladder gaps over stationary sets

2004 ◽  
Vol 69 (2) ◽  
pp. 518-532 ◽  
Author(s):  
Uri Abraham ◽  
Saharon Shelah
Keyword(s):  
Chain Condition ◽  
Finite Support ◽  
Ladder System ◽  
New Type ◽  
Stationary Set

Abstract.For a stationary set S ⊆ ω1, and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is C-Hausdorff. But for every ladder E over ω1 ∖ S there exists a gap with no subgap that is E-Hausdorff.A new type of chain condition, called polarized chain condition, is introduced. We prove that the iteration with finite support of polarized c.c.c. posets is again a polarized c.c.c. poset.

scholarly journals Rebranding Perpustakaan Umum Kota Pasuruan Dalam Upaya Peningkatan Citra Event Story Telling

2019 ◽  
Vol 1 (02) ◽  
pp. 72-76
Author(s):  
Indra Gunawan ◽  
Pujiyanto Pujiyanto ◽  
Fariza Wahyu Arizal
Keyword(s):  
Story Telling ◽  
Stationary Set

Perpustakaan umum kota Pasuruan memiliki suatu kegiatan yang bertujuan untuk mengapresiasi bakat anak – anak usia sekolah dasar di bidang sastra melalui event story telling. Kegiatan tersebut merupakan kegiatan rutin tahunan yang diselenggarakan oleh perpustakaan umum kota Pasuruan sebagai upaya untuk mendekatkan diri terhadap masyarakat. Penggunaan media promosi dalam event story telling yang diselenggarakan oleh perpustakaan umum kota Pasuruan merupakan hal yang dibutuhkan guna menarik perhatian masyarakat luas. Mengingat kurangnya media promosi yang dilakukan oleh pihak perpustakaan umum kota Pasuruan mengakibatkan event tersebut kurang mendapat dukungan terhadap masyarakat. Rancangan yang digunakan untuk mempromosikan event story telling berupa rebranding media promosi dan penambahan media penunjang berupa stationary set dan merchandise. Rebranding media promosi merupakan salah satu solusi guna membantu meningkatkan daya tarik masyarakat terhadap penyelenggaraan event story telling. Penambahan media seperti stationary set dan merchandise tidak hanya digunakan untuk menarik perhatian masyarakat saja, akan tetapi penggunaan media tersebut ditujukan sebagai nilai tambah yang diperlukan agar event tersebut memiliki sebuah identitas tersendiri.

scholarly journals Condition Rating Prediction Using an Interactive Deterioration Model Development Package

2020 ◽  
Vol 10 (24) ◽  
pp. 8946
Author(s):  
Minwoo Chang ◽  
Marc Maguire
Keyword(s):  
Asset Management ◽  
Model Development ◽  
Data Interpretation ◽  
Bridge Inspection ◽  
Explanatory Variables ◽  
Deterioration Model ◽  
Condition Rating ◽  
Initial Dataset ◽  
Stationary Set ◽  
Inspection Data

This paper presents an advanced method to determine explanatory variables required for developing deterioration models without the interference of human bias. Although a stationary set of explanatory variables is ideal for long-term monitoring and asset management, the penalty regression results vary annually due to the innate bias in the inspection data. In this study, weighting factors were introduced to consider the inspection data collected for several years, and the most stationary set was identified. To manage the substantial amount of inspection data effectively, we proposed a software package referred to as the Deterioration Model Development Package (DMDP). The objective of the DMDP is to provide a convenient platform for users to process and investigate bridge inspection data. Using the standardized data interpretation, the user can update an initial dataset for the deterioration model development when new inspection data are archived. The deterministic method and several stochastic approaches were included for the development of the deterioration models. The performances of the investigated methods were evaluated by estimating the error between the predicted and inspected condition ratings; further, this error was used for estimating the most effective number of explanatory variables for a given number of bridges.

The non-compactness of square

2003 ◽  
Vol 68 (2) ◽  
pp. 637-643 ◽  
Author(s):  
James Cummings ◽  
Matthew Foreman ◽  
Menachem Magidor
Keyword(s):  
Stationary Subset ◽  
Supercompact Cardinal ◽  
Stationary Set ◽  
Square Sequences ◽  
Set Of Points ◽  
Type Sequence

This note proves two theorems. The first is that it is consistent to have for every n, but not have . This is done by carefully collapsing a supercompact cardinal and adding square sequences to each ωn. The crux of the proof is that in the resulting model every stationary subset of ℵω+1 ⋂ cof(ω) reflects to an ordinal of cofinality ω1, that is to say it has stationary intersection with such an ordinal.This result contrasts with compactness properties of square shown in [3]. In that paper it is shown that if one has square at every ωn, then there is a square type sequence on the points of cofinality ωk, k > 1 in ℵω+1. In particular at points of cofinality greater than ω1 there is a strongly non-reflecting stationary set of points of countable cofinality.The second result answers a question of Džamonja, by showing that there can be no squarelike sequence above a supercompact cardinal, where “squarelike” means that one replaces the requirement that the cofinal sets be closed and unbounded by the requirement that they be stationary at all points of uncountable cofinality.

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