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	Hyper-Woodin cardinal - Wikipedia, the free encyclopedia
		In axiomatic set theory, hyper-Woodin cardinals are a kind of large cardinals.
		A cardinal κ is called hyper-Woodin iff there exists a normal measure U on κ such that for every set S, the set {λ < κ
		The difference between hyper-Woodin cardinals and weakly hyper-Woodin cardinals is that the choice of U does not depend on the choice of the set S for hyper-Woodin cardinals.
	en.wikipedia.org /wiki/Hyper-Woodin_cardinal (93 words)

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		Cardinal bishops are the bishops of seven sees around Rome (Ostia, Velletri, Porto and Santa Rufina, Albano, Frascati, Palestrina, and Sabina and Poggio Mirteto) and Eastern-rite patriarchs; the first of these in order of creation is dean of the college and ex officio bishop of Ost...
		Guise -> The Second Duke of Guise and the Cardinal of Lorraine Claude's son François de Lorraine, 2d duc de Guise, 1519-63, became conspicuous, at the accession (1547) of Henry II, as the rival for power of Anne, duc de Montmorency.
		An enemy of Cardinal Mazarin, chief minister for the regent Anne of Austria, Retz was prominent in the Fronde against him...
	www.encyclopedia.com /searchpool.asp?target=Woodin+cardinal (482 words)

	Weakly hyper-Woodin cardinal - Wikipedia, the free encyclopedia
		In axiomatic set theory, weakly hyper-Woodin cardinals are a kind of large cardinals.
		A cardinal κ is called weakly hyper-Woodin iff for every set S there exists a normal measure U on κ such that the set {λ < κ
		Ernest Schimmerling, Woodin cardinals, Shelah cardinals and the Mitchell-Steel core model, Proceedings of the American Mathematical Society 130/11, pp.
	en.wikipedia.org /wiki/Weakly_hyper-Woodin_cardinal (122 words)

	Recent Advances in Core Model Theory (Site not responding. Last check: 2007-10-20)
		Woodin's recent refutation of CBH is an important breakthrough, and one major goal of the workshop is to get a good understanding of it.
		In many applications, it is important to construct an inner model of large cardinal hypothesis H under an assumption that is not itself a large cardinal hypothesis.
		In case H is significantly stronger than ``there is one Woodin cardinal'', the connection between large cardinals and models of the axiom of determinacy, or AD, becomes quite important.
	www.math.cmu.edu /users/eschimme/AIM/LongDescription.html (590 words)

	Large cardinal explained (Site not responding. Last check: 2007-10-20)
		In mathematics, a cardinal is called a large cardinal if it belongs to a class of cardinals, the existence of which provably cannot be proved within the standard axiomatic set theory ZFC, if one assumes ZFC itself is consistent.
		Therefore the discussion of large cardinals takes place in a realm of conditional proofs, which (according to the consensus view of logicians) will remain so.
		Erdős cardinals (The existence of the Aleph-1-Erdős cardinal implies the existence of 0#, which implies the consistency of Erdős cardinals for all countable ordinals.)
	www.wordspider.net /la/large-cardinal.html (598 words)

	[No title]
		Solovay has shown that the consistency of AD is equivalent to that of a measurable cardinal; we know that this cannot be proved if set theory is consistent, as it would enable the proof of the consistency of set theory within itself.
		In fact, ZF+AD is equiconsistent with ZFC+"there exist infinitely many Woodin cardinals".
		I'm not going to go into exactly what a Woodin cardinal is, but a number of distinct steps can be identified above measurable and below Woodin.
	www.math.niu.edu /~rusin/known-math/01_incoming/AD (1004 words)

	Woodin cardinal - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-20)
		In set theory, a Woodin cardinal is a cardinal number κ such that for all
		Woodin cardinals are important in descriptive set theory.
		This page was last modified 05:21, 3 October 2005.
	en.wikipedia.org /wiki/Woodin_cardinal (62 words)

	Citations: Combinatorial principles in the core model for one Woodin cardinal - Schimmerling (ResearchIndex) (Site not responding. Last check: 2007-10-20)
		....[38, 48] A particularly striking feature of these core models is that the failure of covering at a singular cardinal for one of the core models yields an inner model with a large cardinal of the strength of that core model.
		In particular, the failure of square or of the singular cardinals hypothesis implies the existence of inner models of fairly large cardinals.
		In his study of core models for Woodin cardinals Schimmerling was able to establish versions of square (and ; that are slightly weaker than....
	citeseer.ist.psu.edu /context/1169411/0 (575 words)

	Hyper-Woodin cardinal weakly hyper-Woodin cardinal iff large cardinal axiomatic set theory cardinal (Site not responding. Last check: 2007-10-20)
		A cardinal κ is called hyper-Woodin iff there exists a normal measure U on κ such that for every set S, the set {λ
		weakly hyper-Woodin cardinals are a kind of large cardinals.
		WOODIN CARDINALS, SHELAH CARDINALS, AND THE MITCHELL-STEEL CORE...
	en.powerwissen.com /8mqAxRfMFpvWj%7C%7CSL%7C%7CTnhH5E%7C%7CSL%7C%7Cg%3D%3D_Hyper-Woodin_cardinal.html (197 words)

	Large cardinal -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		Therefore the discussion of large cardinals takes place in a realm of (Click link for more info and facts about conditional proof) conditional proofs, which (according to the consensus view of logicians) will remain so.
		The following is a list of some types of large cardinals; it is arranged in order of the consistency strength.
		Existence of a cardinal number κ of a given type implies the existence of cardinals of most of the types listed above that type, and for all listed cardinal descriptions φ of lesser consistency strength, V(κ) satisfies "there are unboundedly many cardinals satisfying φ".
	www.absoluteastronomy.com /encyclopedia/l/la/large_cardinal.htm (568 words)

	WOODIN
		"WOODIN" is generally used as a noun (proper) -- approximately 66.67% of the time.
		"WOODIN" is used about 3 times out of a sample of 100 million words spoken or written in English.
		The following table summarizes the usage of "WOODIN" based on a population census conducted in the United States.
	www.websters-online-dictionary.org /definition/WOODIN (422 words)

	Infinite Arithmetic Sets - One-one Mapping
		The cardinal of Z+ is equal to the cardinal of Z- without recourse to the
		The claim that infinite cardinals have parity leads to a contradiction.
		Therefore, it is false that infinite cardinals have parity.
	www.groupsrv.com /science/post-56541.html (3548 words)

	Inner model theory bibliography (Site not responding. Last check: 2007-10-20)
		Indiscernible sequences for extenders and the singular cardinal hypothesis, Ann.
		Combinatorial principles in the core model for one Woodin cardinal, Ann.
		Woodin cardinals, Shelah cardinals, and the Mitchell-Steel core model, to appear in Proc.
	www.logic.univie.ac.at /~rds/bibliography.html (762 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		The covering property implies the "weak covering property": if \alpha \geq \omega_2 is a successor cardinal of L, then the cofinality of \alpha is equal to the cardinality of \alpha.
		One kind of extension is illustrated by: Theorem 1 (Mitchell and Schimmerling) Assume that every set has a sharp and that there is no model with a Woodin cardinal.
		One sees a different approach in: Theorem 3 (Schimmerling and Woodin) If W is an iterable weasel without measurable cardinals, and W-sharp does not exist, then W has the covering property.
	www.amsta.leeds.ac.uk /events/logic97/abstracts/schimmerling.txt (223 words)

	Woodin cardinal -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		Woodin cardinal -- Facts, Info, and Encyclopedia article
		In (The branch of pure mathematics that deals with the nature and relations of sets) set theory, a Woodin cardinal is a (The number of elements in a mathematical set; denotes a quantity but not the order) cardinal number κ such that for all
		Woodin cardinals are important in (Click link for more info and facts about descriptive set theory) descriptive set theory.
	www.absoluteastronomy.com /encyclopedia/w/wo/woodin_cardinal.htm (98 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		It is proved that in the absence of proper class inner models with Woodin cardinals, for each n
		theory of the reals under set forcing in a strong sense) implies there are n strong cardinals in K (where this denotes a suitably defined global version of the core model for one Woodin cardinal as exposed by Steel.
		absoluteness is exactly that of n strong cardinals so that in particular projective absoluteness is equiconsistent with the existence of infinitely many strong cardinals.
	www.elsevier.com /cdweb/journals/01680072/articles/74/3/016800729400041.abstract.en (145 words)

	Woodin cardinal - Encyclopedia Glossary Meaning Explanation Woodin cardinal (Site not responding. Last check: 2007-10-20)
		Woodin cardinal - Encyclopedia Glossary Meaning Explanation Woodin cardinal.
		Here you will find more informations about Woodin cardinal.
		The orginal Woodin cardinal article can be editet
	www.encyclopedia-glossary.com /en/Woodin-cardinal.html (112 words)

	List of tea companies . Bewley's . Tetley . Snapple . Tea
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		A cardinal number cardinal κ is called weakly hyper-Woodin iff for every set S there exists a normal measure U on κ such that the set is in U.
		The difference between hyper-Woodin cardinals and weakly hyper-Woodin cardinals is that the choice...
	www.uk.knowledge-info.org /List_of_tea_companies-UK-0848008-ck (587 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Perhaps the most famous result along these lines is the Martin-Steel theorem, which states that granted the existence of $n$ Woodin cardinals and a measurable cardinal above them, all games with a $\Pi^1_{n+1}$ payoff are determined.
		Thus, the determinacy of length $\omega$ games with certain definable payoff was seen to follow from the existence of large cardinals (above, from the existence of Woodin cardinals).
		For example, \vspace{0.2in} {\bf Theorem} (Neeman): Assume that there exist a cardinal which is strong past a Woodin cardinal, and a measurable cardinal above it.
	www.maths.leeds.ac.uk /events/logic97/abstracts/neeman.txt (401 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-20)
		In mathematics, a weakly compact cardinal is a certain kind of cardinal number; weakly compact cardinals are large cardinals, meaning that their existence can neither be proven nor disproven from the standard axioms of set theory.
		Formally, a cardinal κ is weakly compact iff for every functio..
		In Germanic languages, weak verbs are those verbs that have a regular inflection, in which the stem of a word is not changed by ablaut.
	aynurkece.info /browse.php?title=W/WE/WEA (6067 words)

	Bristol University, Maths Dept, Pure Group, Set Theory
		Let $\kappa$ be a cardinal, and let $H_\kappa$ be the class of sets of hereditary cardinality less than $\kappa$; let $\tau(\kappa)> \kappa$ be the height of the smallest transitive admissible set containing every element of $H_\kappa$.
		We remark that this indeed requires large cardinals, and we obtain: {\bf Theorem} The following are equiconsistent: (i) $ZFC + there exists \kappa a Jonsson cardinal; (ii) $ZFC + there exists M \mbox{ a sufficiently elementary submodel of the universe of sets with reals_M not homeomorphic to the reals.
		In particular we consider what kind of large cardinals are necessary in order that Post's problem for the semi-decidable sets of reals has a negative answer.
	www.stats.bris.ac.uk /~mapdw/settheory.html (1834 words)

	Read about Hyper-Woodin cardinal at WorldVillage Encyclopedia. Research Hyper-Woodin cardinal and learn about ... (Site not responding. Last check: 2007-10-20)
		Research Hyper-Woodin cardinal and learn about Hyper-Woodin cardinal here!
		cardinal κ is called hyper-Woodin iff there exists a
		weakly hyper-Woodin cardinals is that the choice of U does not depend on the choice of the set S for hyper-Woodin cardinals.
	encyclopedia.worldvillage.com /s/b/Hyper-Woodin_cardinal (104 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		These notions correspond to Jonsson and Erdos cardinals, except that the submodel or set of indiscernibles is only required to have ordertype delta.
		Second, we weaken the assumption that the Steel core model exists by showing that if the universe is a generic extension of L[\vec E] and there is no model with at Woodin cardinal then the model L[E] can take the place of the Steel core model.
		It follows as a corollary that if L[\vec E] is a minimal model for a Woodin cardinal then every delta-Jonsson cardinal in L[\vec E] is delta-Erdos.
	www.cs.odu.edu /~dlibug/ups/rdf/xxx/math/9706207.rdf (133 words)

	Publication List-Tetsuya Ishiu (Site not responding. Last check: 2007-10-20)
		We proved that $V=L$ implies the existence of a strong club guessing sequence on every uncountable regular cardinal which is not ineffable.
		We also prove that relative to the existence of a Woodin cardinal, it is consistent that every dual ideal of a tail club guessing filter on $\mu$ is precipitous for an uncountable regular cardinal $\mu$.
		Abstract: We settle a conjecture due to R.L. Blair by proving that it is consistent with Martin's Axiom to have a perfectly normal nonrealcompact space of cardinality $\aleph_{1}$.
	www.math.uci.edu /~tishiu/publications.html (246 words)

	Some interesting problems by Arnold W. Miller
		There is also an analogous problem for the splitting cardinal \mathfrak s due to Malyhin, see Kamburelis and Weglorz [87].
		Woodin has recently shown that the answer is yes if we also assume there is a measurable cardinal.
		is equiconsistent with the failure of the singular cardinal hypothesis.
	at.yorku.ca /i/a/a/i/00.dir (4073 words)

	[No title]
		A measurable cardinal with a closed unbounded set of inaccessibles from $o(\kappa)=\kappa$.
		Mitchell, W. Jónsson cardinals, Erdös cardinals, and the core model.
		Indiscernible sequences for extenders, and the singular cardinal hypothesis.
	www.math.ufl.edu /fac/facmr/Mitchell.html (171 words)

	Logic Colloquium
		We show that fine structural inner models for mild large cardinal hypotheses but below a Woodin cardinal admit forcing extensions where bounded forcing axioms hold and the reals are projectively well-ordered.
		In a core model induction argument, one produces canonical inner models which are correct for statements at a given level of complexity, using core model theory together with the existence of models which are correct at lower levels.
		The pattern of connections between determinacy and large cardinals suggests that there should be games which capture the theory of indiscernible Woodin cardinals.
	www.math.ucla.edu /%7Ehbe/logic.html (3032 words)

	Covering lemma (Site not responding. Last check: 2007-10-20)
		In mathematics, under various anti-large cardinal assumptions, one can prove the existence of the canonical inner model, called the Core Model, that is, in a sense, maximal and approximates the structure of V.
		A covering lemma asserts that under the particular anti-large cardinal assumption, the Core Model exists and is maximal in a way.
		For example, if there is no inner model for a measurable cardinal, then the Dodd-Jensen core model, K
	www.sciencedaily.com /encyclopedia/covering_lemma (207 words)

	LC '98 abstract: M. Zeman (Site not responding. Last check: 2007-10-20)
		We are, however, able to produce a global $\square$ sequence in Jensen's core model for non-overlapping extenders (which can contain one strong cardinal, but not more) by imitating Jensen's original {\bf L}-construction.
		The construction is not as uniform as the above one because of the failure of the above mentioned condensation lemma; it is also not clear whether one can have the condensation-coherent version of $\square$ in this larger model.
		At present, it is not clear how to generalize the construction in higher core models (up to one Woodin cardinal), since there the correspondence fails to be $1-1$: to every mouse we can have more protomice and the best known version of $\square$ in these models is Schimmerling's $\square^{<\omega}_\kappa$, which is genuinely weaker than $\square_\kappa$.
	www.math.cas.cz /~lc98/abstracts/Zeman.html (662 words)

	Large cardinal Other types of large cardinals axiomatic set theory ZFC strongly inaccessible cardinal Mahlo cardinal ... (Site not responding. Last check: 2007-10-20)
		Large cardinal Other types of large cardinals axiomatic set theory ZFC strongly inaccessible cardinal Mahlo cardinal unfoldable cardinal subtle cardinal Shelah cardinal huge cardinal rank-into-rank
		Large jobs to small, Cardinal completes its list of services with precision leveling and alignment, metal...
		Welcome to Cardinal Golf Club The Cardinal Golf Club proudly states that "Cardinal is where the public...
	en.powerwissen.com /08WOxwzBQRFCI7XcNuuGfg%3D%3D_Large_cardinal.html (297 words)

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