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Topic: Successor cardinal

In the News (Tue 2 Dec 08)

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	Infinite Ink: Cardinal Numbers
		Since all well-ordered cardinals are ordinals, sometimes I use ordinal notation for a cardinal or vice versa.
		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.
	www.ii.com /math/cardinals (1276 words)

	Limit cardinal - Wikipedia, the free encyclopedia
		With the cardinal successor operation defined, we can define a limit cardinal in analogy to that for limit ordinals: λ is a (weak) limit cardinal if λ is not a successor cardinal, i.e.
		Despite the similarity in terminology and concept with limit ordinal, being a limit cardinal is a much stronger condition, because the cardinal successor operation is much more powerful, in the infinite case, than the ordinal successor operation (so we're not just defining something synonymous).
		is a successor cardinal if and only if α is a successor ordinal, hence also a limit cardinal if and only if α is a limit ordinal.
	en.wikipedia.org /wiki/Limit_cardinal (549 words)

	Successor cardinal - Wikipedia, the free encyclopedia
		In the theory of cardinal numbers, we can define a successor operation similar to that in the ordinal numbers.
		In the infinite case, the successor operation skips over many ordinal numbers; in fact, every infinite cardinal is a limit ordinal.
		Therefore, the successor operation on cardinals gains a lot of power in the infinite case (relative the ordinal successorship operation), and consequently the cardinal numbers are a very "sparse" subclass of the ordinals.
	en.wikipedia.org /wiki/Successor_cardinal (234 words)

	Cardinal O'Connor, 80, Dies; Forceful Voice for Vatican (Site not responding. Last check: 2007-10-18)
		Cardinal O'Connor came to New York in 1984 in a glare of publicity and a flurry of controversy, a relatively unknown Roman Catholic bishop from Pennsylvania who was suddenly catapulted into the church's most visible post in the United States.
		By contrast, Cardinal O'Connor's willingness to joust with public officials and project the church into public debates recalled the years from 1939 to 1967, when the archdiocesan headquarters of Cardinal Francis Spellman was known as the Powerhouse for the leverage the church wielded in city affairs.
		And if Cardinal O'Connor could sometimes still affect city policies with a few phone calls to some politicians, in Cardinal Spellman's day, or so it was widely believed, the calls would have been initiated by the politicians themselves, who were careful to check their plans with the Powerhouse.
	partners.nytimes.com /library/national/regional/050400ny-cardinal-oconnor.html (4194 words)

	PlanetMath: cardinal number
		Cardinal numbers have the property that for every set
		, there exists a unique cardinal number having the same number of elements as
		This is version 4 of cardinal number, born on 2002-01-05, modified 2007-01-23.
	planetmath.org /encyclopedia/Cardinal.html (55 words)

	Rome Diary: An Account by Bishop Hubbard
		Cardinal Francis George of Chicago is a fellow member of a committee to plan the next special assembly for the American bishops, to be held in the summer of 1999.
		Indeed, the Pope as the successor of Peter is the visible fount of unity for the Church and exercises the primacy of teaching authority among all the bishops in the world.
		Cardinal Ratzinger stressed, however, that this is not to denigrate the role of women in the Church; that there are two dimensions to ministry: the Petrine and Marian.
	www.evangelist.org /evv/bish0398.htm (12065 words)

	Zenit News Agency - The World Seen From Rome (Site not responding. Last check: 2007-10-18)
		Cardinal Tomko believes that these "testimonies are also full of hope for the development and spiritual growth that opens the heart to the mission and nourishes missionary cooperation.
		Bishop Egan was born in Oak Park, Illinois, in 1932, and was ordained a priest in 1958, after studies at St. Mary of the Lake Seminary in Mundelein, Illinois, and the Pontifical North American College in Rome.
		Cardinal O'Connor apparently did not approve of the appointment, sending a letter to the priests of the diocese making it clear that Bishop Egan was not his choice.
	www.zenit.org /english/archive/0005/ZE000511.html (3461 words)

	[No title]
		Cardinal Leasing, Inc., was a lessor of tractors and van trailers, with drivers.
		Cardinal's ownership and management were the same as Redway's, and until October 1982 Cardinal did business only with Redway.
		During the existence of Redway and Cardinal as debtors in possession, Redway and Cardinal continued to use the firm, and personnel from the firm prepared the reports that Cardinal and Redway submitted to the court.
	www.nlrb.gov /nlrb/shared_files/decisions/301/301-139.txt (17689 words)

	Infinite Ink: Cardinal Numbers
		Since all well-ordered cardinals are ordinals, sometimes I use ordinal notation for a cardinal or vice versa.
		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.
	ii.best.vwh.net /math/cardinals (1276 words)

	Archdiocese of New York - About Saint Patrick's Cathedral (Site not responding. Last check: 2007-10-18)
		Cardinal Hayes completed an extensive renovation of the interior between 1927 and 1931 when the great organ was installed and the sanctuary was enlarged.
		The exterior was restored during the episcopate of Cardinal Spellman who saw to the completion of the stained glass windows as well as a new main altar and baldachin.
		During the years of John Cardinal O'Connor's episcopate, extensive renovations have been made to maintain the structural integrity of the building, including replacement of much of the roof, exterior steps, replastering of the walls in the transepts, repair of stained glass and refinishing the transept doors.
	www.ny-archdiocese.org /pastoral/cathedral_about.html (508 words)

	Boston.com / News / World / Europe / Politics, challenges to church to guide choice of successor
		Over these next two weeks, the cardinals will have a chance to size one another up, meeting daily as the College of Cardinals assumes collective oversight of the global church and the Vatican bureaucracy during this interregnum.
		Scholars who study papal transitions say history suggests that the cardinals will probably look for an older man as the next pope -- probably someone between 65 and 75 years old -- in order to increase the odds that the next papacy will be relatively short after the 26-year papacy of John Paul II.
		That is because during a long papacy, power tends to concentrate in Rome; a short papacy would allow power to devolve back to the local church and would function as a kind of transition period.
	www.boston.com /news/world/europe/articles/2005/04/04/politics_challenges_to_church_to_guide_choice_of_successor (454 words)

	The Papacy
		Appointed cardinal in 1991, he is a conservative who may still be able to appease liberal factions.
		The Nigerian cardinal, a leading church figure in Africa, is a close friend of the pope's and has performed a crucial role in improving the Vatican's dialogue with Muslim, Buddhist and Hindu groups.
		Known as "the Panzer Cardinal," the conservative Ratzinger is powerful in the Vatican but may be too close to the pope for the cardinals' taste.
	www.time.com /time/daily/special/papacy/succession.html (813 words)

	Cardinal's successor known as Mr. Fix-It (Site not responding. Last check: 2007-10-18)
		BOSTON -- Cardinal Bernard Law's resignation unfolded against the backdrop of a cold and gloomy Friday the 13th in Rome.
		Montalvo would be expected to consult other American cardinals and bishops before making a recommendation to the pope.
		"I'm of course very sad for the cardinal," said the Rev. John Ahearn, a former rectory housemate of Lennon at St. Mary's of the Assumption Parish in Brookline.
	www.eagletribune.com /news/stories/20021214/FP_001.htm (977 words)

	Vienna cardinal accused of pedophilia dies (Site not responding. Last check: 2007-10-18)
		Groer was cardinal of Vienna from 1986 until 1995, when allegations first surfaced that he had sexually molested students at an all-male Catholic boarding school in the early 1970s.
		Groer's successor, Cardinal Christoph Schoenborn, urged Austrians to find a way to put the affair behind them and bury any lingering bitterness along with Groer.
		Groer, a conservative Benedictine priest who ran a retreat center before he was appointed cardinal, had applied for retirement in 1994, when he turned 75, but John Paul left him in his post.
	www.telegram.com /static/crisisinthechurch/032503.html (605 words)

	Pope John Paul’s successor: German Cardinal likely candidate
		The dean of the College of Cardinals is slowly emerging as a consensus candidate to succeed the late Pope, John Paul II.
		Cardinal Carlo Maria Martini, the former archbishop of Milan is also in the running for the Catholic Church's top job.
		The other German cardinals, Karl Lehmann of Mainz and Vatican-based Walter Kasper, are reportedly against his election for the top post.
	www.earthtimes.org /articles/show/2399.html (421 words)

	Cardinal presents successor to lead historic basilica - Examiner.com
		BALTIMORE (Map, News) - More than three decades of Baltimore’s Catholic leadership were in the sanctuary of the Basilica of the Assumption in downtown Baltimore for Thursday’s noontime Mass as Cardinal William Keeler introduced his successor, Archbishop Edwin O’Brien, at his first public ceremony.
		Keeler’s predecessor, retired Archbishop William Borders, 94 and moving slowly, also was one of the vested concelebrants, who included all four auxiliary bishops, to welcome their new leader.
		After the Mass, Keeler, wearing a cardinal’s red biretta and cassock with a white surplice, haltingly left the sanctuary following the other bishops and priests, with a cane in one hand and his other on the arm of a priest.
	www.examiner.com /a-826454~Cardinal_presents_successor_to_lead_historic_basilica.html?cid=rss-Baltimore (605 words)

	Catholic Church :: Pope accepts Cardinal Sin retirement (Site not responding. Last check: 2007-10-18)
		Cardinal Sin’s resignation and the designation of Archbishop Rosales as his successor was officially announced by the Vatican in Rome at noon yesterday.
		Cardinal Sin will continue to govern the Archdiocese of Manila as apostolic administrator with the power of ordinary bishop until his successor is formally brought into office.
		The cardinal submitted his letter of resignation after his 75th birth anniversary — the age of retirement for bishops and non-bishops — in accordance with the Canon Law last Aug. 31.
	religionnewsblog.com /4438-Pope_accepts_Cardinal_Sin_retirement.html (554 words)

	The Catholic Standard - News (Site not responding. Last check: 2007-10-18)
		Cardinal McCarrick announced that the region's more than one-half million Catholics had pledged $185 million for the capital campaign, which will endow the archdiocese's educational, charitable, multicultural and parish outreach for now and in future years.
		The Archdiocese of Washington was established in 1939, and eight years later it separated from the Archdiocese of Baltimore.
		In the post-World War II "baby boom," Cardinal Patrick O'Boyle led the archdiocese in a time of great growth, as families throughout the area made generous contributions to the new parishes and schools being built in their communities.
	www.cathstan.org /news/current/1.shtml (403 words)

	Mario Derksen's TRADITIONAL INSIGHT Column (nov18mdi.htm)
		The cardinals had been gathered in conclave since the evening of October 25, and apparently they had already elected a Pope the very next day when white smoke was seen blowing from the chimney around noontime.
		Pius XII had appointed Cardinal Giuseppe Siri as his desired successor.[7] Siri was rabidly anti-Communist, an intransigent traditionalist in matters of church doctrine, and a skilled bureaucrat.
		This was a burden on several of the Cardinals who were in their nineties and in failing health, but in deference to the new Pope they all stayed.
	www.dailycatholic.org /issue/04Nov/nov18mdi.htm (4750 words)

	Rubin, Slipyj exchange indicates Vatican warning to Ukrainians (12/26/82)
		Cardinal Rubin's letter, dated July 6, was written on the recommendation of Pope John Paul II.
		Cardinal Rubin also criticized the pastoral letter written on the occasion of the patriarch's 90th birthday, which was addressed, in the first place, to the faithful in Ukraine.
		The patriarch also noted that the tone of Cardinal Rubin's letter is offensive to the Ukrainian Catholic Church and to him personally as head of that Church.
	www.ukrweekly.com /Archive/1982/528209.shtml (950 words)

	Cultural Catholic - Pope Nicholas II
		Before his death, Pope Stephen IX instructed the cardinals not to proceed with the election of his successor until Cardinal Hildebrand returned from his mission to the imperial court in Germany.
		Cardinal Gerard was born about 980 at Chevron in the Savoy province of France and was installed on January 24, 1059 as Pope Nicholas II coronate successor to Pope Stephen IX.
		Pope Nicholas II was a reform prelate and set controls for the election and conduct of popes by assembling a synod of 113 bishops on April 13, 1059 whose first order of business was to declare the election of Pope Benedict X unconstitutional.
	www.culturalcatholic.com /PopeNicholasII.htm (392 words)

	~The Siri Fact, Pope Gregory XVII~
		This was the sign the cardinals had failed to elect on the first two ballots, at nightfall white smoke billowed from the slender chimney for a full five minutes.
		Pius XII had appointed Cardinal Guiseppe Siri as his desired successor.(7) Siri was rabidly anti-Communist, an intransigent traditionalist in matters of church doctrine, and a skilled bureaucrat who had been personally trained in the intricacies of Vatican finances by Bernardino Nogara.
		The conservative cardinals believed that Roncalli, at the age of seventy-eight, was too old to wreak havoc within the Vatican and would only serve as a "guardian pope" until the next conclave.
	www.theimmaculateheart.com /gregoryXVII.htm (2952 words)

	CNS STORY: U.S. Cardinal Szoka says he offered blessing when he visited pope
		Speaking while Pope John Paul was still alive, the cardinal said he trusts that the Holy Spirit will help the 117 cardinals who are eligible to enter the conclave and elect Pope John Paul's successor.
		Cardinal Szoka said the pope's personal secretary phoned him April 1 and asked him to come to the papal apartment; the cardinal arrived about 10 minutes later.
		Cardinal Szoka, a Polish-American and the former archbishop of Detroit, said he told the pope in Polish that he had celebrated Mass for him that morning and that he was praying for him.
	www.catholicnews.com /data/stories/cns/0501907.htm (452 words)

	Guardian Unlimited \| Special reports \| Cautious style has left no clear successor
		Cardinal Hume was spiritual head of the English and Welsh Roman Catholic church for so long that his successor will struggle to be judged in his own right - rather than as just better or worse than the cardinal.
		Cardinal Hume was the eloquent, pious patrician-priest of the television age, and even those to whom his views were alien have become used to seeing and hearing him offer moral counsel.
		Some Catholics argue that Cardinal Hume's success as a national figure has come at the expense of the day to day running of the Westminster diocese and that Westminster does not want another monk.
	www.guardian.co.uk /religion/Story/0,2763,205106,00.html (617 words)

	Clancy loses papal conclave voting right (Site not responding. Last check: 2007-10-18)
		Sydney's retired Cardinal Edward Clancy turned 80 on Friday, which means he loses his right to vote for the next pope, and Australia will have only two electors at the papal conclave.
		Cardinal Clancy, who was an auxiliary bishop in Sydney and Archbishop of Canberra and Goulburn, before he was appointed Archbishop of Sydney, was elevated to cardinal in 1988.
		In 1970 Paul VI reformed the college of cardinals by increasing the number of electors to 120, not counting those 80 years of age and over who were excluded as electors.
	www.cathnews.com /news/312/100.html (313 words)

	Westminster_Cathedral (Site not responding. Last check: 2007-10-18)
		Not to be confused with Westminster Abbey of the Church of England, Westminster Cathedral is the seat of the Archbishop of Westminster, currently Cormac Cardinal Murphy-O'Connor, shepherd of the Archdiocese of Westminster and primate of the nation's Catholics.
		In the late 19th century, the Catholic Church hierarchy had only recently been restored in the United Kingdom, and it was in memory of Cardinal Wiseman (who died in 1865, and was the first Archbishop of Westminster from 1850) that the first substantial sum of money was raised for the new Cathedral.
		In 1995, at the invitation of Cardinal Basil Hume, it was visited by the Queen, this being the first visit of a reigning monarch of the United Kingdom to a Catholic liturgy for several hundred years.
	www.freecaviar.com /search.php?title=Westminster_Cathedral (716 words)

	The Papal Successor: Cardinal Joseph Ratzinger - News Story - WGAL Lancaster
		The new pope is chosen by cardinals who are 80 years old or younger.
		A new pope is elected by the College of Cardinals.
		Cardinals are next-highest ranking members of the church after the pope.
	www.wgal.com /news/4393690/detail.html (1128 words)

	ipedia.com: Aleph number Article (Site not responding. Last check: 2007-10-18)
		The cardinality of the natural numbers is aleph-null, the next larger cardinality is aleph-one, then comes aleph-two and so on.
		A set has cardinality Aleph-null if and only if it is countably infinite, which is the case if and only if it can be put into a direct one-to-one correspondence (see bijection) with the integers.
		That it is consistent with ZFC was demonstrated by Kurt Gödel; in 1940; that it is independent of ZFC was demonstrated by Paul Cohen in 1963.
	www.ipedia.com /aleph_number.html (628 words)

	Cardinal Richelieu (Site not responding. Last check: 2007-10-18)
		Cardinal Richelieu (George Arliss) dominating King Louis XIII of France.
		1589 -- on his deathbed Henry III recognizes Henry, King of Navarre and leader of the Huguenots, as his successor, who, as Henry IV, is the first Bourbon to become King of France.
		Richelieu's successor, Cardinal Mazarin, brought it to an end in 1653.
	members.aol.com /snuffy1186/cardinal.html (537 words)

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