Concerning ultrafilters on ultrapowers

1987 ◽  
Vol 52 (1) ◽  
pp. 149-151
Author(s):  
J. M. Henle
Keyword(s):  
Supercompact Cardinal ◽  
Partition Relation ◽  
Great Abundance ◽  
Axiom Of Determinacy ◽  
History Of

This paper concerns ultrafilters on a cardinal γ extending the filter of λ-closed, unbounded sets, λ < γ. The history of these ultrafilters is closely connected with that of the axiom of determinacy (AD). Solovay noticed first that, under AD, there was such an ultrafilter for γ = ℵ1; λ = ω. Later, Kleinberg found that the existence of such ultrafilters followed from the partition relation γ → (γ)λ+λ. Specific instances of this and more powerful relations on cardinals were then proved from AD by Martin, Kunen, Paris, and others. The axiom of determinacy was recently shown consistent with ZF relative to something less than a supercompact cardinal by Martin and Steel. Solovay's and Kleinberg's results were actually stronger, and we discuss this at the end of the paper. Good references for these results include [K2] and [KM].We are interested here in the case where γ is the ultrapower of a strong partition cardinal κ (a cardinal satisfying for all α < κ). Such cardinals exist in great abundance assuming AD, and in fact, if sufficiently many cardinals are strong, then AD holds in L[R] [KKMW].

Some consequences of an infinite-exponent partition relation

1977 ◽  
Vol 42 (4) ◽  
pp. 523-526 ◽  
Author(s):  
J. M. Henle
Keyword(s):  
Set Theory ◽  
Measurable Cardinal ◽  
Large Cardinals ◽  
Axiom Of Choice ◽  
Partition Relation ◽  
Basic Theorem ◽  
Axiom Of Determinacy ◽  
Ramsey’S Theorem ◽  
Partition Relations ◽  
Dependent Choice

Beginning with Ramsey's theorem of 1930, combinatorists have been intrigued with the notion of large cardinals satisfying partition relations. Years of research have established the smaller ones, weakly ineffable, Erdös, Jonsson, Rowbottom and Ramsey cardinals to be among the most interesting and important large cardinals in set theory. Recently, cardinals satisfying more powerful infinite-exponent partition relations have been examined with growing interest. This is due not only to their inherent qualities and the fact that they imply the existence of other large cardinals (Kleinberg [2], [3]), but also to the fact that the Axiom of Determinacy (AD) implies the existence of great numbers of such cardinals (Martin [5]).That these properties are more often than not inconsistent with the full Axiom of Choice (Kleinberg [4]) somewhat increases their charm, for the theorems concerning them tend to be a little odd, and their proofs, circumforaneous. The properties are, as far as anyone knows, however, consistent with Dependent Choice (DC).Our basic theorem will be the following: If k > ω and k satisfies k→(k)k then the least cardinal δ such that has a δ-additive, uniform ultrafilter. In addition, if ACω is assumed, we will show that δ is greater than ω, and hence a measurable cardinal. This result will be strengthened somewhat when we prove that for any k, δ, if then .

scholarly journals Hemimycale columella (Bowerbank): a short description and history of the species

1955 ◽  
Vol 34 (3) ◽  
pp. 553-557 ◽  
Author(s):  
G. R. Forster
Keyword(s):  
Deep Water ◽  
Systematic Position ◽  
Short Description ◽  
Great Abundance ◽  
Small Minority ◽  
Unique Character ◽  
History Of ◽  
Siliceous Spicules

These notes arise from the difficulty met with in identifying a pinkish encrusting sponge which has been frequently collected by hand from rocks at 5–10 fathoms. The sponge was at first identified, by a process of elimination, with the deep water genus Inflatella. Fortunately some preparations were shown to Dr Lévi at Roscoff to whom the species was at once familiar as Stylotella columella (Bowerbank). It was then found that this species had been described originally by Bowerbank from an Exmouth specimen, and subsequendy by Topsent from both south and west coasts of France. Topsent found the unusual, if not unique, character of this sponge in possessing, besides siliceous spicules, a great abundance of calcareous granules. These granules are almost certainly the ‘gemmules’ described and figured by Bowerbank. De Laubenfels in 1928 collected one specimen from Plymouth Sound which he identified as Stylotella columella; but proposed (1932) that the species should be included in the genus Prianos Gray. Burton in 1934 renamed the species Hemimycale columella, figuring the spicules as styles. Arndt (1935) returned to Stylotella and retained Burton's figure of the spicules. As the styles have been found, so far, only as a small minority amongst the spicules, it has been thought worth while to provide a further description; and to discuss the differing views on the systematic position of the species.

scholarly journals Culicoides (Diptera: Ceratopogonidae) of Colombia: records from the collection of insects of medical importance from National Institute of Health

2021 ◽  
Author(s):  
Erika Santamaria ◽  
Marco Súarez ◽  
Ricardo Ortiz Gallego ◽  
Patricia Fuya ◽  
Geraldine Páez ◽  
...  
Keyword(s):  
Public Health ◽  
Geographical Distribution ◽  
Great Abundance ◽  
Vector Borne Diseases ◽  
New Information ◽  
History Of ◽  
Vector Borne ◽  
Medical Importance

The collection of insects of medical importance from the National Institute of Health (Colombia) INS, was started in 1934 with the aim of being an institutional and national repository of the biodiversity of insects involved in vector-borne diseases of importance in public health. Today, the entomological collection includes more than 7.500 specimens. The ceratopogonids insects are one of the Groups of Diptera that conform this collection. Within the Ceratopogonidae family, are the insects of the genera Culicoides which are relevant in public health because of the nuisance caused by their bites when they are presented in great abundance and because of their role as transmitters of several agents (virus, protozoa and nematodes) that causes diseases to the humans and to the animals (Mullen 2002, Kettle 1995). Brief of the Ceratopogonidae insects (Diptera: Ceratopogonidae) found in the collection, is presented here. A total of 801 individuals of this family rest in the collection, mainly adult of the genus Culicoides (90%). The collection is the result of the effort of several researchers through the history of the Group of Entomology (INS). These researchers collected ceratopogonids when they went to different transmission scenarios of the vector-borne diseases in Colombia, with the purpose of making the entomological characterizations. The effort of the researchers also included the processing, assembly, and identification of the specimens in the laboratory. New information about the geographical distribution of 39 species of the genera Culicoides appears for Colombia.

scholarly journals A case of peritoneal-pericardial leak in a 19-year-old patient on peritoneal dialysis

2021 ◽  
Vol 4 (2) ◽  
pp. 129-135
Author(s):  
Meryem Birrou ◽  
Mina Agrou ◽  
Hasnae Guerrouj ◽  
Rabia Bayahia ◽  
Loubna Benamar
Keyword(s):  
Peritoneal Dialysis ◽  
Progressive Increase ◽  
Great Abundance ◽  
Pericardial Drainage ◽  
Glucose Levels ◽  
Fluid Analysis ◽  
History Of ◽  
Glucose Plasma ◽  
Radio Tracer

We report a case of a peritoneal-pericardial leak in peritoneal dialysis.A 19-year-old patient, with no history of heart disease, with unkown chronic kidney disease, treated with continuous ambulatory peritoneal dialysis (CAPD) for 10 months. complained of chest pain and tachycardia, revealing pericardial effusion of great abundance. Pericardial drainage was necessary. The fluid analysis was a transudate with glucose levels 5 times higher than glucose plasma levels. A peritoneal scintigraphy was performed and showed a distribution of the radio-tracer in the peritoneal cavity without any image of a leak. With clinical and especillay biological arguments, the patient was diagnosed with a peritoneal-pericardial leak.After pericardial drainage and temporary switch to hemodialysis, automated peritoneal dialysis was resumed with progressive increase in volumes, without recurrence of the leak after a 6 months follow-up.

Precambrian–Cambrian boundary candidate, Meishucun, Jinning, Yunnan, China

1984 ◽  
Vol 121 (3) ◽  
pp. 143-154 ◽  
Author(s):  
Xing Yusheng ◽  
Luo Huilin
Keyword(s):  
Yunnan Province ◽  
Close Association ◽  
Great Abundance ◽  
Small Shelly Fossils ◽  
Great Progress ◽  
History Of ◽  
Stratotype Section ◽  
Bedding Surface ◽  
Carbonate Deposits ◽  
Made In

AbstractBeing located in Jinning County, Yunnan Province, approximately 103° E, 25° N, the Meishucun section has a long history of study, convenient accessibility, mild spring-like climate all the year round and good exposures of the relevant strata. In the particular area there occur monofacial transitional carbonate deposits of marine origin, yielding in great abundance both small shelly fossils and trace fossils, which are present in close association and in some cases on the same bedding surface. The sequence of biotic assemblages is clearly evident and can be used for wide intercontinental correlation.In the lower part of the Qiongzhusi Stage, stratigraphically higher, there appear the oldest trilobites, archaeostracods and Baltisphaeridium characteristic of the Early Cambrian.During the last six years great progress has been made in the study of the particular section through lithostratigraphic, biostratigraphic, geochronological, magnetostratigraphic and seismostratigraphic approaches, thus making the Meischucun Stage and the Sinian–Cambrian boundary stratotype section in the Meishucun area a Chinese candidate for global stratotype section and point for the Precambrian–Cambrian boundary.

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