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1

Borel sets without perfectly many overlapping translations

Rosłanowski Andrzej, Shelah Saharon

Reports on Mathematical Logic

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2019

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Vol. 54

3--43

EN

We study the existence of Borel sets B ⊆ ω2 admitting a sequence ηα : α<λ of distinct elements of ω2 such that (ηα +B)∩(ηβ +B) ≥ 6 for all α, β < λ but with no perfect set of such η’s. Our result implies that under the Martin Axiom, if ℵα < c, α<ω1 and 3 ≤ ι<ω, then there exists a Σ0 2 set B ⊆ ω2 which has ℵα many pairwise 2ι–nondisjoint translations but not a perfect set of such translations. Our arguments closely follow Shelah [7, Section 1].

2

Forcing for First-Order Languages from the Perspective of Rasiowa-Sikorski Lemma

Czelakowski J.

Fundamenta Informaticae

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2017

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Vol. 156, nr 3/4

255--280

EN

The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski [9]. The central idea, developed in this paper, consists in constructing first-order models from individual variables. The key notion of a Rasiowa–Sikorski set of formulas for an arbitrary countable language L is examined. Each Rasiowa–Sikorski set defines a countable model for L. Conversely, every countable model for L is determined by a Rasiowa-Sikorski set. The focus is on constructing Rasiowa-Sikorski sets by applying forcing techniques restricted to Boolean algebras arising from the subsets of the set of atomic formulas of L.

3

Modelling of the teeth separation states in gears considering diesel engine forcing features

Dyk J.

Diagnostyka

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2016

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Vol. 17, No. 4

73--78

EN

In the paper the possibility of the direct application of forcing computed function based on the elementary model of the diesel engine regarding issues of the rattle vibrations in modelling of gears was introduced. In this way the simulated indicator diagrams were created. After that, build diagrams were used to calculate tangential forces and torques operating in the drive system. Considering only the torsional vibrations, these calculated values of torques can be introduced as the forcing that are acting on gears inside of the gearbox. The presented in the article different models enable us to diagnose and analyse the neutral gear rattle. The forcing of the diesel engine introduced at the low range of rotation speeds is one of the most important parameters which may cause, within the clearance, the creation of the phenomenon of a lack of contact of the regular meshing of teeth, and, as a consequence vibrations and the difficult acoustic effects connected with rattle.

PL

W pracy, dla zagadnień dotyczących drgań rattle w modelowaniu przekładni, przedstawiono możliwość zastosowania bezpośredniego wyliczania funkcji wymuszającej silnika na podstawie elementarnego modelu uwzględniającego zmiany ciśnienia czterosuwowego silnika o zapłonie samoczynnym. Stworzono w ten sposób symulowane wykresy indykatorowe, które wykorzystano do obliczeń przebiegów sił stycznych i momentów działających w układzie napędowym. Zakładając jedynie drgania skrętne obliczany moment wprowadzić można jako wejściowe wymuszenie przekładni znajdujących się wewnątrz skrzyni biegów. Przedstawiono różne modele opisujące klekotanie zębów w biegu luzem, które umożliwiają diagnozę powstania tego zjawiska. Wymuszenie od silnika działające w niskim zakresie prędkości obrotowych jest jednym z ważniejszych parametrów, który spowodować może, w obrębie luzu międzyzębnego, powstanie zjawiska utraty prawidłowego styku zębów, a w konsekwencji drgań i uciążliwych efektów akustycznych związanych z klekotaniem.

4

Drogi i bezdroża ograniczania zasolenia oraz oczyszczania wód kopalń Górnośląskiego Zagłębia Węglowego

Pluta I.

Przegląd Górniczy

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2012

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T. 68, nr 3

125--131

PL

W pracy opisano sposoby i metody, jakie w ciągu ponad sześćdziesięciu lat zastosowano, aby ograniczyć negatywny wpływ wód pochodzących z kopalń Górnośląskiego Zagłębia Węglowego. Celem było wskazanie pozytywnych osiągnięć z określeniem kierunku prowadzenia dalszych badań i prac nad zagospodarowaniem i oczyszczaniem zasolonych wód kopalnianych.

EN

The article describes the ways and methods which were applied during more than sixty years in order to reduce the negative impact of waters originating from mines in the Upper Silesian Coal Basin. The objective was the indication of positive achievements with the determination of the direction of conducting of further works regarding the management and purification of salty mine waters.

5

A Note on Forcing and Type Theory

Coquand T., Jaber G.

Fundamenta Informaticae

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2010

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Vol. 100, nr 1/4

43-52

EN

The goal of this note is to show the uniform continuity of definable functional in intuitionistic type theory as an application of forcing with dependent type theory.

6

Specializing Aronszajn tree and preserving some weak diamonds

Mildenberger H., Shelah S.

Journal of Applied Analysis

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2009

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Vol. 15, nr 1

47-78

EN

We show that [wzór) together with CH and "all Aronszajn trees are special" is consistent relative to ZFC. The weak diamond for the covering relation of Lebesgue null sets was the only weak diamond in the Cichori diagramrne for relations whose consistency together with "all Aronszajn trees are special" was not yet settled. Our forcing proof gives also new proofs to the known consistencies of several other weak diamonds stemming from the Cichori diagramme together with "all Aronszajn trees are special" and CH. The main part of our work is an application [15, Chapter V, §§ 1-7] for a special completeness system, such that we have a genericity game. Thus we show new preservation properties of the known forcings.

7

Properness without elementaricity

Shelah S.

Journal of Applied Analysis

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2004

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Vol. 10, nr 2

169-289

EN

We present reasons for developing a theory of forcing notions which satisfy the properness demand for countable models which are not necessarily elementary sub-models of some (H(x),∈ ). This leads to forcing notions which are "reasonably" definable. We present two specific properties materializing this intuition: nep (non-elernentary properness) and snep (Souslin non-elementary properness) and also the older Souslin proper. For this we consider candidates (countable models to which the definition applies). A major theme here is "preservation by iteration", but we also show a dichotomy: if such forcing notions preserve the positiveness of the set of old reals for some naturally defined c.c.c. ideal, then they preserve the positiveness of any old positive set hence preservation by composition of two follows. Last but not least, we prove that (among such forcing notions) the only one commuting with Cohen is Cohen itself; in other words, any other such forcing notion make the set of old reals to a meager set. In the end we present some open problems in this area.

8

HIROMB, an operational eddy-resolving model for the Baltic Sea

Funkquist L.

Biuletyn Instytutu Morskiego w Gdańsku

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2001

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Vol. 28, No. 2

7--16

EN

HIROMB is a 3-dimensional baroclinic model of the North Sea and the Baltic Sea, designed for daily operational use. The model is mainly developed by Eckhard Kleine at the German Federal Maritime and Hydrographic Agency (BSH) in Hamburg, Germany, and is based on a similar model, running in operational mode at that institution. The operational forecasts at SMHI starled already in 1995 with a daily 24-hour forecast and were later extended to 48 hours. The model is forced by SMHI's operational atmospheric model (HIRLAM), but also by river runoff from an operational hydrological model and wave radiation stress from a wind wave model. The present version of the model is set up on a nested grid, where a 12 nautical mile (nm) grid covers the whole area, while Skagerrak, Kattegat, the Belt Sea and the Baltic Sea are covered with a 1 nm grid. A parallelized version of the model has been developed and runs on a distributed memory parallel computer.