scholarly journals Simple forcing notions and forcing axioms

1997 ◽  
Vol 62 (4) ◽  
pp. 1297-1314
Author(s):  
Andrzej Rosłanowski ◽  
Saharon Shelah
Keyword(s):  
Forcing Axioms ◽  
Starting Point ◽  
Cohen Real ◽  
Large Continuum ◽  
The Continuum

In the present paper we are interested in simple forcing notions and Forcing Axioms. A starting point for our investigations was the article [4] in which several problems were posed. We answer some of those problems here.In the first section we deal with the problem of adding Cohen reals by simple forcing notions. Here we interpret simple as of small size. We try to establish as weak as possible versions of Martin Axiom sufficient to conclude that some forcing notions of size less than the continuum add a Cohen real. For example we show that MA(σ-centered) is enough to cause that every small σ-linked forcing notion adds a Cohen real (see Theorem 1.2) and MA(Cohen) implies that every small forcing notion adding an unbounded real adds a Cohen real (see Theorem 1.6). A new almost ωω-bounding σ-centered forcing notion ℚ⊚ appears naturally here. This forcing notion is responsible for adding unbounded reals in this sense, that MA(ℚ⊚) implies that every small forcing notion adding a new real adds an unbounded real (see Theorem 1.13).In the second section we are interested in Anti-Martin Axioms for simple forcing notions. Here we interpret simple as nicely definable. Our aim is to show the consistency of AMA for as large as possible class of ccc forcing notions with large continuum. It has been known that AMA(ccc) implies CH, but it has been (rightly) expected that restrictions to regular (simple) forcing notions might help.

scholarly journals Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170612 ◽  
Author(s):  
Malena I. Español ◽  
Dmitry Golovaty ◽  
J. Patrick Wilber
Keyword(s):  
Continuum Model ◽  
Domain Walls ◽  
Three Dimensional ◽  
Variational Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Starting Point ◽  
Continuum Modelling ◽  
Three Dimensional System ◽  
The Continuum

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

scholarly journals Forcing axioms and the continuum hypothesis

2013 ◽  
Vol 210 (1) ◽  
pp. 1-29 ◽  
Author(s):  
David Asperό ◽  
Paul Larson ◽  
Justin Tatch Moore
Keyword(s):  
Continuum Hypothesis ◽  
Forcing Axioms ◽  
The Continuum

scholarly journals Bounded forcing axioms and the continuum

2001 ◽  
Vol 109 (3) ◽  
pp. 179-203 ◽  
Author(s):  
David Asperó ◽  
Joan Bagaria
Keyword(s):  
Forcing Axioms ◽  
The Continuum

PAIRING AND SPONTANEOUS POLARIZATION IN DENSE HYDROGEN

1999 ◽  
Vol 13 (05n06) ◽  
pp. 595-605 ◽  
Author(s):  
N. W. ASHCROFT
Keyword(s):  
Charge Density ◽  
Electron Gas ◽  
Density Wave ◽  
Functional Integral ◽  
Integral Representations ◽  
Many Body ◽  
Starting Point ◽  
The Many ◽  
A Charge ◽  
The Continuum

The many-body problem associated with dense hydrogen can represented by the standard interacting electron gas problem (complete with compensating charge continuum) augmented by the proton equivalent and a coupling between the two. This viewpoint is useful as a starting point in the pursuit of ground-state instabilities (particularly the onset of a charge density wave) as a function of the continuum charge density, and even more generally in the identification of forms for the fields required to establish a thermodynamic treatment via coherent state functional integral representations of the partition function for dense hydrogen.

Meschonnic’s Theory of Rhythm, his Key Concepts and their Relation

2019 ◽  
pp. 15-31
Author(s):  
Marko Pajević
Keyword(s):  
Human Life ◽  
Full Understanding ◽  
Art And Literature ◽  
Starting Point ◽  
Key Concepts ◽  
Way Of Thinking ◽  
The Continuum

This chapter introduces into the key concepts of Meschonnic’s theory. Basing the conception of language on the sign represents an obstacle to the awareness of certain elements of human life, especially to a full understanding of what language or art do. Meschonnic’s poetics of the continuum and of rhythm criticizes the sign based on Benveniste’s terms of rhythm and discourse, developing an anthropology of language. Rhythm, for Meschonnic, is no formal metrical but a semantic principle, each time unique and unforeseeable. As for Humboldt, his starting point is not the word but the ensemble of speech. The poem, then, is a process of transformation, a way of thinking, and rhythm is form in movement. Thus, Meschonnic’s poetics attempts to thematize the intelligibility of presence. Art and literature raise our awareness of this continuous. This poetic thinking is a necessary counterforce against all institutionalization.

scholarly journals Tożsamość czynu jako podstawa różnicowania mechanizmów redukujących odpowiedzialność karną

2017 ◽  
Vol 43 ◽  
pp. 107-129
Author(s):  
Jacek Giezek
Keyword(s):  
Criminal Liability ◽  
Binding Model ◽  
Reduction Mechanisms ◽  
Starting Point ◽  
The Subject ◽  
Normative Criteria ◽  
The One ◽  
Legal Judgement ◽  
The Continuum

The Identity of an act as a basis for differentiation of mechanisms reducing criminal responsibilityOur starting point is the view, well grounded in the dogmatics of criminal law, that the separation of a criminal off ence as an entity judged from a legal standpoint is based upon both ontic and normative criteria. On the one hand, the basis for an act, anchored in reality, is the behaviour of a subject, on the other hand, what part of it we consider a single object of legal judgement is decided by the legislator. The situation becomes more complicated whenever the judgement of a particular part of a subject’s behaviour is determined by the realisation of the features of at least two prohibited acts. The criteria of unity of an act — apart from full or partial identity of time, in which at least two sets of features of prohibited acts are realised, are highly vague. One could probably refrain from searching for them, has it not been for the fact that the presence of a single act — or multiple acts — is the basis for the currently binding model of reduction mechanisms. If those mechanisms were to rationalise criminal liability, the basis of their use should consist of entirely normative criteria, based, for example, on those that we use for objective ascription of the result. A model of mechanisms of this kind could be determined by the quantity and quality of the violated rules of conduct, or, to use a diff erent phrase, the multiplicity of sources of risk generated by the subject. A positive consequence of such rearrangement could be the possibility of abandoning the concept of an act as an object of legal judgement, selected from the continuum of behaviour, with a precisely determined timeframe.

Forcing

2018 ◽  
Author(s):  
John P. Burgess
Keyword(s):  
Set Theory ◽  
Continuum Hypothesis ◽  
Axiom Of Choice ◽  
Forcing Axioms ◽  
Martin's Axiom ◽  
Martin’S Axiom ◽  
The Axiom Of Choice ◽  
The Continuum

The method of forcing was introduced by Paul J. Cohen in order to prove the independence of the axiom of choice (AC) from the basic (ZF) axioms of set theory, and of the continuum hypothesis (CH) from the accepted axioms (ZFC = ZF + AC) of set theory (see set theory, axiom of choice, continuum hypothesis). Given a model M of ZF and a certain P∈M, it produces a ‘generic’ G⊆P and a model N of ZF with M⊆N and G∈N. By suitably choosing P, N can be ‘forced’ to be or not be a model of various hypotheses, which are thus shown to be consistent with or independent of the axioms. This method of proving undecidability has been very widely applied. The method has also motivated the proposal of new so-called forcing axioms to decide what is otherwise undecidable, the most important being that called Martin’s axiom (MA).

Toward an Understanding of Borderland Processes

2006 ◽  
Vol 71 (1) ◽  
pp. 77-100 ◽  
Author(s):  
Bradley J. Parker
Keyword(s):  
Dynamic Interaction ◽  
Fundamental Importance ◽  
Conceptual Frameworks ◽  
Regional Comparison ◽  
Academic Fields ◽  
Starting Point ◽  
The Common ◽  
Frontier Studies ◽  
Boundary Dynamics ◽  
The Continuum

Although the study of frontiers is of fundamental importance to a variety of academic fields and subdisciplines, few researchers have proposed terminology, models or conceptual frameworks that allow a cross-disciplinary supra-regional comparison of frontier dynamics. In this paper I take three steps toward rectifying this situation. First, I propose a simplified lexicon that is widely applicable across disciplinary, temporal and regional divides. This lexicon is meant to be a starting point in defining boundary situations. Second, lay out a model, called the “continuum of boundary dynamics.” This model is meant to aid researchers in characterizing various types of boundary situations. And third, propose a model, called the “borderland matrix” with which to visualize the dynamic interaction between different categories of boundaries. This model is meant to aid researchers in isolating processes that occur in borderlands. It is my position that only through systematic comparisons of boundary situations at various times and locations can we hope to understand the processes that take place in borderlands. By defining and characterizing boundary situations and then isolating the processes taking place there, I believe that we will come much closer to understanding the common and unique themes that make frontier studies a central interregional and interdisciplinary subject of study.

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