scholarly journals Forcing with adequate sets of models as side conditions

2017 ◽  
Vol 63 (1-2) ◽  
pp. 124-149 ◽  
Author(s):  
John Krueger
Keyword(s):  
Models As Side Conditions ◽  
Adequate Sets

scholarly journals Coherent adequate sets and forcing square

2014 ◽  
Vol 224 (3) ◽  
pp. 279-300 ◽  
Author(s):  
John Krueger
Keyword(s):  
Adequate Sets

scholarly journals Multi-level gradient-based methods and parametrisation in aerodynamic shape design

2008 ◽  
pp. 169-197
Author(s):  
Massimiliano Martinelli ◽  
François Beux
Keyword(s):  
Shape Design ◽  
Inviscid Flows ◽  
Shape Representations ◽  
Aerodynamic Shape ◽  
Gradient Based ◽  
Multi Level ◽  
Grid Points ◽  
New Formulation ◽  
Adequate Sets ◽  
Compact Shape

The present study focuses on multi-level approaches in the context of discrete gradient-based methods for aerodynamic shape design. More precisely, the minimisation is done alternatively on different control subspaces according to multigrid-like cycles, providing at each sub-level a particular gradient preconditioning. Starting from an existing multi-level gradient-based formulation associated to shape grid-points coordinates, a possible generalisation to more compact shape representations is proposed through the construction of adequate sets of embedded shape sub-parametrisations. The behaviour of the new formulation is illustrated on different 2D inverse problems for inviscid flows.

Models as Side Conditions

Set Theory ◽  
1998 ◽  
pp. 99-107 ◽  
Author(s):  
Piotr Koszmider
Keyword(s):  
Models As Side Conditions

scholarly journals Coherent adequate forcing and preserving CH

2015 ◽  
Vol 15 (02) ◽  
pp. 1550005 ◽  
Author(s):  
John Krueger ◽  
Miguel Angel Mota
Keyword(s):  
Set Theory ◽  
General Framework ◽  
Adequate Sets

We develop a general framework for forcing with coherent adequate sets on [Formula: see text] as side conditions, where [Formula: see text] is a cardinal of uncountable cofinality. We describe a class of forcing posets which we call coherent adequate type forcings. The main theorem of the paper is that any coherent adequate type forcing preserves CH. We show that there exists a forcing poset for adding a club subset of [Formula: see text] with finite conditions while preserving CH, solving a problem of Friedman [Forcing with finite conditions, in Set Theory: Centre de Recerca Matemática, Barcelona, 2003–2004, Trends in Mathematics (Birkhäuser-Verlag, 2006), pp. 285–295.].

On Adequate Sets of Multi-valued Logic

2021 ◽  
Author(s):  
Daizhan Cheng ◽  
Jun-e Feng ◽  
Jianli Zhao ◽  
Shihua Fu
Keyword(s):  
Adequate Sets
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