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# Topic: Regular cardinal

###### In the News (Fri 24 May 13)

 PlanetMath: cofinality is regular, because the union of countably many countable sets is countable. More generally, all infinite successor cardinals are regular. (this being the smallest uncountable aleph which is provably not the cardinality of the continuum). planetmath.org /encyclopedia/RegularCardinal.html   (207 words)

 PlanetMath: cardinality of the continuum , so it could be either a successor cardinal or a limit cardinal, and either a regular cardinal or a singular cardinal. "cardinality of the continuum" is owned by yark. This is version 10 of cardinality of the continuum, born on 2004-03-15, modified 2004-05-28. planetmath.org /encyclopedia/CardinalityOfTheContinuum.html   (158 words)

 Hebrew Cardinal Numbers A cardinal number (mispar) tells how many things there are (in a set), for example, one, two, three, and so on. Cardinal numbers can occur in the construct state to indicate a link between the number and the noun it modifies. These numbers are basically plural forms of the regular (feminine) cardinal numbers. www.hebrew4christians.com /Grammar/Unit_Eight/Cardinal_Numbers/cardinal_numbers.html   (464 words)

 Infinite Ink: Cardinal Numbers A cardinal that is not a finite cardinal is an infinite cardinal. In ZF it is possible to have a Dedekind-finite cardinal that is not a finite cardinal. 1 is the ordinal successor of a, is the cardinal successor of aleph www.ii.com /math/cardinals   (1276 words)

 Springer Online Reference Works Cantor defined the cardinal number of a set as that property of it which remains after abstracting the qualitative nature of its elements and their ordering. Every cardinal number less than the first uncountable strongly-inaccessible cardinal number is non-measurable (Ulam's theorem), and the first measurable cardinal number is certainly strongly inaccessible. However, the first measurable cardinal number is considerably larger than the first uncountable strongly-inaccessible cardinal number (Tarski's theorem). eom.springer.de /c/c020370.htm   (632 words)

 New Axioms for Set Theory A good reason is non-rigidity, that is the existence of a nontrivial elementary embedding of V into M if the cardinals existed: Such embedding raises the question as to why the universe is V rather than M; metaphorically speaking, such embedding implies that V is not held together by its structure. An interesting strengthening of the principle of undefinability of well-orderings for regular cardinals is that for every regular infinite cardinal κ, every set of subsets of κ that is ordinal definable from κ ordinal parameters either has cardinality at most κ or contains a perfect subset. The defining property of regular cardinals is that for every regular cardinal κ, every partition of κ into less than κ sets contains a set of cardinality κ. web.mit.edu /dmytro/www/ProposedAxioms.htm   (1541 words)

 jfkcyberinfinite This arises from the definition of cardinality, in that there is no one-to-one mapping from alef-one to omega. As a last note, an ordinal a is regular if it cannot be represented as the sum of less than a ordinals less than a. Among the large cardinals are the inaccessible cardinals, hyperinaccessible cardinals, Mahlo cardinals, indescribable cardinals, ineffable cardinals, partition cardinals, Ramsey cardinals, measurable cardinals, strongly compact cardinals, supercompact cardinals, and finally (at present), extendible cardinals, each being an order of thinking (a quantum leap) greater than their predecessor. www.cage.curtin.edu.au /~jfk/infinity.html   (2310 words)

 Major League Baseball : News : Baseball Perspectives And the Cardinals had been blessed in the rotation not only with talent and determination but with health. The Cardinals were without four regulars for a long stretch and still played well enough to have baseball's best record nearly five months into the season. So the Cardinals ask Jason Marquis, on a seven-game losing streak, to move up a day, to fill a gap, and this is what happens -- his first career shutout. stlouis.cardinals.mlb.com /NASApp/mlb/news/article_perspectives.jsp?ymd=20050827&content_id=1186232&vkey=perspectives&fext=.jsp   (947 words)

 The Roman Catholic Diocese of Westminster - Cardinal CARDINAL CORMAC MURPHY-O'CONNOR, the Archbishop of Westminster and President of the Bishops’ Conference of England and Wales, was born on 24 August 1932 in Reading, Berkshire, the fifth son of Dr. George Murphy-O'Connor and his wife, Ellen. The Cardinal is an honorary bencher of the Inner Temple and in August 2001 was created a Freeman of the City of London. The Basilica houses the relics of St Catherine of Siena, doctor of the Church and one of the Patron Saints of Europe, the tomb of the Dominican Friar Blessed Fra Angelico, the Patron Saint of Artists, the renowned 'Figure of the Risen Christ' by Michelangelo and frescoes by Fra Filippo Lippi. www.rcdow.org.uk /cardinal/default.asp?content_ref=4   (993 words)

 Warehousing Service Cardinal is able to adjust manufacturing schedules and maintain predetermined stock levels for rapid delivery. Cardinal's commitment to service is equal to its quest for quality. The people at Cardinal are constantly working with the employees of our clients in a never ending effort to find the most efficient and economical ways to manufacture their products. www.cardinalmfg.com /WarehousingService/warehousingservice.html   (126 words)

 [No title] In fact, for every "function" E from cardinals to cardinals that satisfies these two requirements (weak monotonicity, and the cf(E(x)) > x) there is a model of ZFC that has E(x)=2^x. Later, Easton in "Powers of regular cardinals" extended this result to all regular cardinals simultaneously: the only restriction on phi -> 2^phi for phi regular is that the function be nondecreasing and not have cofinality(2^phi) = phi. Aleph_1 having countable cofonality means that aleph_1 (as the set of all lesser ordinals using the von Neumann definition of ordinals) is a countable union of countable sets. www.math.niu.edu /~rusin/known-math/99/luzin_easton   (1129 words)

 Papers.html   (Site not responding. Last check: 2007-10-22) The axioms are generalizations of large cardinal axioms and their descriptive set theoretic consequences include the consequences of large cardinals such as the Axiom of Determinacy. The second paper introduces a maximally strong forcing axiom "Martin's Maximum" and shows that is consistent, settles the values of the continuum, the singular cardinals hypothesis, implies that the non-stationary ideal on the first uncountable cardinal is saturated, and (using results of Woodin) that supercompact cardinals imply that every set in L(R) is Lebesgue Measurable. Assuming appropriate large cardinals, it contains many results about when a new equivalence class can be added to a homogeneously Suslin equivalence relation by forcing, and deduces as a consequence that many generic embeddings and ideals imply that the definable continuum is small. www.math.uci.edu /sub2/Foreman/homepage/newpapers.html   (2671 words)

 Women's Crew Wraps Up Regular Season :: Cardinal took on the Bears at the 31st Annual Big Row. Cardinal took on the Bears at the 31st Annual Big Row. Redwood Shores, CA - The Stanford Cardinal competed against the California Bears in the 31st annual Big Row at Redwood Shores. This concludes the regular racing schedule for the 2006 racing season. gostanford.cstv.com /sports/w-crew/recaps/042906aaa.html   (118 words)

 Major League Baseball : News : Baseball Perspectives   (Site not responding. Last check: 2007-10-22) LOUIS -- Down to the very last out, the stands were still full of Cardinals fans, all of them standing in red-clad unison, flashbulbs popping all around for the entire ninth inning. They stayed for more than an hour after the game, soaking in a video presentation and cheering former stars, then staying to cheer their current stars, who came back on the field for the ultimate curtain call. The tribute marked the end of a month of tributes for the place and the people who played here, with Cardinals from the past and present taking in their last few sips of Busch Stadium from September to October. stlouis.cardinals.mlb.com /NASApp/mlb/news/article_perspectives.jsp?ymd=20051019&content_id=1255124&vkey=perspectives&fext=.jsp   (737 words)

 Infinite Ink Glossary: Cofinality, Regular, & Singular If a is regular then a is a cardinal. In ZFC, it is not possible to prove that there is an uncountable regular limit cardinal. Cardinal numbers especially regular, singular, weakly_inaccessible, and inaccessible cardinals. www.ii.com /glossary/cofinality_regular_singular   (157 words)

 RV.Net Open Roads Forum: Fifth-Wheels: Cardinal Platinum's I did notice that the Platinum is 8" taller in the rear then the Cardinal, and that is has resident sized sinks in the kitchen and bathroom and has the Alphastone solid counter tops. Along with what you mentioned, the Cardinal Platinum has a larger view window and 7000# axles with 8 lug wheels which is not on any other as well as the upgrade trim package which includes slide Fascia and stainless microwave, oven, and stainless front fridg. Example.....the standard cardinal 34 RLT had 20" deep cabinets in the rear which we needed but when the Platinum arrived they were 10" deep but prettier (Big Deal). www.rv.net /forum/Index.cfm/fuseaction/thread/tid/14232123.cfm   (799 words)

 Freshman's 3 goals lift Stanford / Janusz, Cardinal bounce Broncos from NCAA tournament Roger Levesque, the leading scorer on the Stanford men's soccer team, was on the sideline yesterday, forced merely to watch his team play Santa Clara in the second round of the NCAA tournament because he drew a red card in the Cardinal's last regular-season game. The Cardinal (17-1-1) now will host Portland, a 1-0 winner over Washington, at the same Stanford campus site in the third round Friday night. Janusz got his second score, after assists by Todd Dunivant and Matt Moses, at the 23:24 mark of the first half, and the Cardinal appeared to be cruising. www.sfgate.com /cgi-bin/article.cgi?file=/chronicle/archive/2001/11/26/SP150836.DTL&type=printable   (502 words)

 Sacco Earns Three Varsity Lacrosse Letters ECSU concluded the regular season ranked fourth in New England and tied for 14th nationally. Among the team's wins were a 18-12 win over Wesleyan University - the Cardinal's only regular season loss - as well as victories over perennial New England powers Trinity (+11 - 6), Colby (+ 16 - 7) and Babson (+8 - 2). Through the regular season, Eastern was ranked second nationally in scoring offense (17.13) third in scoring margin (+10.56) and 10th in scoring defense (6.56). www.antonnews.com /westburytimes/2001/07/20/sports   (273 words)

 washingtonpost.com: AAA NORTHWESTERN REGION : Who's In The skinny: Coach Andy Gray has joked this season that his Indians are not much to look at during warmups, with a relatively small team that might not invoke much fear in an opponent. The skinny: Surprising young Freedom emerged as the favored second team out of the Cardinal when it won nine of its final 10 regular season games and Hylton lost five of its last six. But Hylton could not be counted out, thanks to 7-foot-2 center Matt Hewson, a Delaware signee who totaled 22 points in the regular season finale to halt the losing streak, and 23 in the district semifinal win over Freedom. www.washingtonpost.com /ac2/wp-dyn/A37108-2005Feb19?language=printer   (1144 words)

 Surfin' The Audio Waves With Wavelength Audio's Cardinal X-1 Monoblock Amplifiers by Steven R. Rochlin After hearing many great comments concerning the updates that have been made to the Cardinal, it was decided to send my units back to their maker for complete updates to X-1 status. I built Steve Guttenberg's amplifier on a Cardinal XS chassis was the WE437A input tube used in the original Triton and still used in the Napoleon. Since I made the original idea on the Cardinal platform and this stayed with the Cardinal number of tubes 3, I decided to declare this the new Cardinal X1, because in my book this is the best circuit for 300B. www.enjoythemusic.com /magazine/equipment/0702/wavelengthcardinalx1.htm   (2492 words)

 Springer Online Reference Works The generalization of this equality to arbitrary cardinal numbers is called the generalized continuum hypothesis (GCH): For every ordinal number is an arbitrary uncountable regular cardinal number given in advance, and It is known that for regular cardinal numbers eom.springer.de /c/c025790.htm   (492 words)

 [No title]   (Site not responding. Last check: 2007-10-22) A weakly inaccessible cardinal is a regular limit cardinal. A (strongly) inaccessible cardinal is a regular *strong* limit cardinal; m is a strong limit cardinal if n < m implies 2^n < m. By the way, if 2^Aleph0 is a RVMC, it follows that 2^m = 2^Aleph0 for every infinite cardinal m < 2^Aleph0; it particular, 2^Aleph-omega = 2^Aleph0, and so we have 2^Aleph0 = AlephN where N = 2^Aleph0 = 2^Aleph-omega. www.math.niu.edu /~rusin/known-math/00_incoming/GCH   (283 words)

 Pujols worthy of runner-up While his recent 30-game hitting streak, longest by a Cardinal in 53 years, brought him increased attention, there is so much more. Pujols already is the first Cardinal to have three successive years of 40-plus doubles since Musial from 1952-54. If he does it again this year, he'll be the first Cardinal to lead his team three years in a row since George Hendrick did it four straight from 1980-83. www.sfgate.com /cgi-bin/article.cgi?file=/c/a/2003/08/31/SP293291.DTL&type=printable   (729 words)

 untitled Regular = Likely to be seen on every or almost every trip. Irregular = Regular but not seen on every or almost every time on trips to this area. Seasonally regular = Likely to be seen on every or almost every trip during the correct season. www.birdinghawaii.co.uk /Forestandtrailreports2.htm   (332 words)

 APS 15th Annual Convention Program Book :: Submission Detail We hypothesized that participants who were in the early stages of starting a program of regular exercise would think about health images more frequently than participants who were not interested in exercising or who were long-term regular exercisers. Furthermore, we hypothesized that participants who thought frequently about health images would be more likely to increase their levels of regular exercise over time. Cardinal, B. The stages of exercise scale and stages of exercise behavior in female adults. www.psychologicalscience.org /cfs/program/view_submission.cfm?Abstract_ID=3294   (417 words)

 The Birdhouse Digest - Cardinals' Trivia When was the last time the Cardinals had the same eight regular starters from one year to the next? #11  What St. Louis Cardinal has over 3000 hits but never won a batting title?  Only 3 men ever had more than 3000 hits but never won a batting title, the other two were Eddie Collins and Robin Yount. #17  Which Cardinal pitcher has had the best ERA in the past 60 years. www.thestlcardinals.com /trivia.html   (516 words)

 Non-normality numbers by S. Dolecki, T. Nogura, R. Peirone and G. M. Reed It is proved that for every cardinal \kappa, there exists a completely regular topology of non-normality and strong non-normality \kappa; for every uncountable regular cardinal \kappa, there exists a (completely regular) Moore space of non-normality and cardinality \kappa. On the other hand, for every pair of cardinals \kappa < \lambda there exists a completely regular topology of strong non-normality \kappa and non-normality greater than \lambda. As an answer to a question of Umberto Marconi, it is proved that the non-normality number of every separable regular topology with a closed discrete subset of cardinality continuum is at least continuum. at.yorku.ca /b/a/a/l/66.htm   (169 words)

 Vegicaps®Soft capsules - Health & Nutrition - Cardinal Health   (Site not responding. Last check: 2007-10-22) Research among consumers, using three brands of unidentified cod liver oil capsules – a Cardinal Health soft gelatin, a competitive soft non-gelatin and Vegicaps® Soft – recorded attitudes and impressions on first sight, and sampled each of the products over a three day period. Participants were shown three unidentified products and asked to visually compare each of them with the cod liver oil they take regularly. Vegicaps® Soft compares very favourably with the historical proven quality of the regular Cardinal Health soft gelatin capsule. www.cardinal.com /PTS/vitamins/vegicaps/comments.asp   (226 words)

 Catholic World News : Ugandan cardinal bids government respond to concerns of aid donors Kampala, May. 04, 2005 (CWNews.com) - Ugandan Cardinal Emmanuel Wamala has urged President Yoweri Museveni to address the concerns of foreign-aid donors, after Britain withdrew its regular support. Cardinal Wamala observed to local reporters that "when the donors withhold aid from Uganda, it is the grassroots, the would-be beneficiaries, who suffer more than government officials." He urged the government to be more responsive to the concerns being expressed by donor nations. The donors who supply 52 percent of Uganda's government budget have been steadily increasing pressure on the Museveni government to promote real democratic reforms. www.cwnews.com /news/viewstory.cfm?recnum=36946   (250 words)

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