scholarly journals Strongly compact cardinals and the continuum function

2021 ◽  
pp. 103013
Author(s):  
Arthur W. Apter ◽  
Stamatis Dimopoulos ◽  
Toshimichi Usuba
Keyword(s):  
Continuum Function ◽  
Strongly Compact Cardinals ◽  
The Continuum

The tree property and the continuum function below ℵω

2018 ◽  
Vol 64 (1-2) ◽  
pp. 89-102
Author(s):  
Radek Honzik ◽  
Šárka Stejskalová
Keyword(s):  
Tree Property ◽  
Continuum Function ◽  
The Continuum

scholarly journals On supercompactness and the continuum function

2014 ◽  
Vol 165 (2) ◽  
pp. 620-630
Author(s):  
Brent Cody ◽  
Menachem Magidor
Keyword(s):  
Continuum Function ◽  
The Continuum

scholarly journals A Study of L2 Approximations in Atomic Scattering

1990 ◽  
Vol 43 (5) ◽  
pp. 485 ◽  
Author(s):  
AT Stelbovics ◽  
T Winata
Keyword(s):  
Convergence Rates ◽  
Basis Set ◽  
Matrix Elements ◽  
Close Coupling ◽  
Set Size ◽  
Atomic Scattering ◽  
Impact Ionisation ◽  
Three Body ◽  
Continuum Function ◽  
The Continuum

The approximation of Coulomb continuum functions by an L 2 basis is studied using a Laguerre� function basis which can be extended to completeness. Also studied is the convergence rate of L2 approximations to Born matrix elements for electron impact ionisation as a function of basis�set size. This important class of matrix elements occurs in pseudo�state close-coupling calculations, accounting for scattering to the three�body continuum. Convergence rates in both cases are derived analytically and confirmed numerically. We find that the rate of pointwise convergence of L2 expansions to the continuum function is slow, and of conditional type; however, it is proven that the corresponding ionisation matrix elements converge geometrically, Our result agrees with the behaviour observed in pseudo�state calculations.

scholarly journals Consecutive Singular Cardinals and the Continuum Function

2013 ◽  
Vol 54 (2) ◽  
pp. 125-136
Author(s):  
Arthur W. Apter ◽  
Brent Cody
Keyword(s):  
Singular Cardinals ◽  
Continuum Function ◽  
The Continuum

DEFINABILITY OF SATISFACTION IN OUTER MODELS

2016 ◽  
Vol 81 (3) ◽  
pp. 1047-1068 ◽  
Author(s):  
SY-DAVID FRIEDMAN ◽  
RADEK HONZIK
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
Inaccessible Cardinal ◽  
Infinitary Logic ◽  
First Order ◽  
Admissible Sets ◽  
Transitive Model ◽  
Regular Cardinals ◽  
Continuum Function ◽  
The Continuum

AbstractLet M be a transitive model of ZFC. We say that a transitive model of ZFC, N, is an outer model of M if M ⊆ N and ORD ∩ M = ORD ∩ N. The outer model theory of M is the collection of all formulas with parameters from M which hold in all outer models of M (which exist in a universe in which M is countable; this is independent of the choice of such a universe). Satisfaction defined with respect to outer models can be seen as a useful strengthening of first-order logic. Starting from an inaccessible cardinal κ, we show that it is consistent to have a transitive model M of ZFC of size κ in which the outer model theory is lightface definable, and moreover M satisfies V = HOD. The proof combines the infinitary logic L∞,ω, Barwise’s results on admissible sets, and a new forcing iteration of length strictly less than κ+ which manipulates the continuum function on certain regular cardinals below κ. In the appendix, we review some unpublished results of Mack Stanley which are directly related to our topic.

LARGE CARDINALS AND LIGHTFACE DEFINABLE WELL-ORDERS, WITHOUT THE GCH

2015 ◽  
Vol 80 (1) ◽  
pp. 251-284
Author(s):  
SY-DAVID FRIEDMAN ◽  
PETER HOLY ◽  
PHILIPP LÜCKE
Keyword(s):  
Fixed Point ◽  
Measurable Cardinal ◽  
Large Cardinals ◽  
Inaccessible Cardinal ◽  
Proper Class ◽  
Supercompact Cardinals ◽  
Image Position ◽  
Class Forcing ◽  
Continuum Function ◽  
The Continuum

AbstractThis paper deals with the question whether the assumption that for every inaccessible cardinal κ there is a well-order of H(κ+) definable over the structure $\langle {\rm{H}}({\kappa ^ + }), \in \rangle$ by a formula without parameters is consistent with the existence of (large) large cardinals and failures of the GCH. We work under the assumption that the SCH holds at every singular fixed point of the ℶ-function and construct a class forcing that adds such a well-order at every inaccessible cardinal and preserves ZFC, all cofinalities, the continuum function, and all supercompact cardinals. Even in the absence of a proper class of inaccessible cardinals, this forcing produces a model of “V = HOD” and can therefore be used to force this axiom while preserving large cardinals and failures of the GCH. As another application, we show that we can start with a model containing an ω-superstrong cardinal κ and use this forcing to build a model in which κ is still ω-superstrong, the GCH fails at κ and there is a well-order of H(κ+) that is definable over H(κ+) without parameters. Finally, we can apply the forcing to answer a question about the definable failure of the GCH at a measurable cardinal.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

Observations of the continuum near the galactic centre

1967 ◽  
Vol 31 ◽  
pp. 405
Author(s):  
F. J. Kerr
Keyword(s):  
Galactic Centre ◽  
The Past ◽  
Centre Region ◽  
The Continuum

A continuum survey of the galactic-centre region has been carried out at Parkes at 20 cm wavelength over the areal11= 355° to 5°,b11= -3° to +3° (Kerr and Sinclair 1966, 1967). This is a larger region than has been covered in such surveys in the past. The observations were done as declination scans.

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