scholarly journals Uniqueness of means in the Cohen model

2019 ◽  
Vol 60 (1) ◽  
pp. 49-60
Author(s):  
 Kalajdzievski Damjan ◽  
Steprāns Juris
Keyword(s):  
Cohen Model

Murray G. Bell. Spaces of ideals of partial functions. Set theory and its applications, Proceedings of a conference held at York University, Ontario, Canada, Aug. 10–21,1987, edited by J. Streprāns and S. Watson, Lecture notes in mathematics, vol. 1401, Springer-Verlag, Berlin etc. 1989, pp. 1–4. - Alan Dow. Compact spaces of countable tightness in the Cohen model. Set theory and its applications, Proceedings of a conference held at York University, Ontario, Canada, Aug. 10–21,1987, edited by J. Streprāns and S. Watson, Lecture notes in mathematics, vol. 1401, Springer-Verlag, Berlin etc. 1989, pp. 55–67. - Peter J. Nyikos. Classes of compact sequential spaces. Set theory and its applications, Proceedings of a conference held at York University, Ontario, Canada, Aug. 10–21,1987, edited by J. Streprāns and S. Watson, Lecture notes in mathematics, vol. 1401, Springer-Verlag, Berlin etc. 1989, pp. 135–159. - Franklin D. Tall. Topological problems for set-theorists. Set theory and its applications, Proceedings of a conference held at York University, Ontario, Canada, Aug. 10–21,1987, edited by J. Streprāns and S. Watson, Lecture notes in mathematics, vol. 1401, Springer-Verlag, Berlin etc. 1989, pp. 194–200.

1991 ◽  
Vol 56 (2) ◽  
pp. 753-755
Author(s):  
Judith Roitman
Keyword(s):  
Set Theory ◽  
Partial Functions ◽  
Compact Spaces ◽  
Countable Tightness ◽  
Lecture Notes ◽  
Model Set ◽  
Cohen Model ◽  
Sequential Spaces

scholarly journals A special class of almost disjoint families

1995 ◽  
Vol 60 (3) ◽  
pp. 879-891 ◽  
Author(s):  
Thomas E. Leathrum
Keyword(s):  
Ordered Sets ◽  
Minimum Cardinality ◽  
Disjoint Family ◽  
Open Questions ◽  
Consistency Results ◽  
The Family ◽  
Almost Disjoint ◽  
Cohen Model ◽  
Almost Disjoint Family ◽  
Almost Disjoint Families

AbstractThe collection of branches (maximal linearly ordered sets of nodes) of the tree <ωω (ordered by inclusion) forms an almost disjoint family (of sets of nodes). This family is not maximal — for example, any level of the tree is almost disjoint from all of the branches. How many sets must be added to the family of branches to make it maximal? This question leads to a series of definitions and results: a set of nodes is off-branch if it is almost disjoint from every branch in the tree; an off-branch family is an almost disjoint family of off-branch sets; and is the minimum cardinality of a maximal off-branch family.Results concerning include: (in ZFC) , and (consistent with ZFC) is not equal to any of the standard small cardinal invariants or = 2ω. Most of these consistency results use standard forcing notions—for example, in the Cohen model.Many interesting open questions remain, though—for example, whether .

L'axiome de normalité pour les espaces totalement ordonnés

1990 ◽  
Vol 55 (1) ◽  
pp. 277-283 ◽  
Author(s):  
Labib Haddad ◽  
Marianne Morillon
Keyword(s):  
Ordered Set ◽  
Axiom Of Choice ◽  
Order Topology ◽  
Cohen Model ◽  
The Axiom Of Choice ◽  
Linearly Ordered Set

AbstractWe show that the following property (LN) holds in the basic Cohen model as sketched by Jech: The order topology of any linearly ordered set is normal. This proves the independence of the axiom of choice from LN in ZF, and thus settles a question raised by G. Birkhoff (1940) which was partly answered by van Douwen (1985).

Support structures for the axiom of choice

1971 ◽  
Vol 36 (1) ◽  
pp. 28-38 ◽  
Author(s):  
David Pincus
Keyword(s):  
General Theory ◽  
Set Theory ◽  
Axiom Of Choice ◽  
Embedding Theorems ◽  
Support Structures ◽  
Support Structure ◽  
Cohen Model ◽  
The Axiom Of Choice

The notion of “support” was introduced by Mostowski in [4] in order to prove that a certain universe satisfied the ordering principle but not the axiom of choice. The notion was refined in [3] and in [1] it was shown to be satisfied in a certain Cohen model of full ZF set theory. This paper is an axiomatic study of universes whose undefined relations are ∈ and a “support structure”, T.In §2 the general theory is introduced and the universes of [4] and [1] are characterized. §3 examines a more complicated universe which will be used in [5] to show that in many cases a consistency in full ZF set theory may be proven directly by the methods of [4]. The embedding theorems of §4 are crucial to this application.

Modelling the far wings of collision-induced translational spectral profiles

2001 ◽  
Vol 79 (5) ◽  
pp. 801-811 ◽  
Author(s):  
W Glaz ◽  
G C Tabisz
Keyword(s):  
Quantum Calculations ◽  
Line Shapes ◽  
Langevin Approach ◽  
Spectral Profiles ◽  
Cohen Model

By comparing three model spectral profiles to precise line shapes obtained from quantum calculations, we assess the suitability of the various models for describing the far wings of translational collision-induced spectra. A profile obtained based on a generalized Langevin approach can give a better fit to the quantum shape than the widely used Birnbaum–Cohen model; the fit given by the six-parameter extended Birnbaum–Cohen profile proves to be the best of all three functions. PACS No.: 32.70Jz

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