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{{for|a list of examples|list of large cardinal properties}}
==  ちょうど彼の呼吸から10以内に取りに言っ ==
In the mathematical field of [[set theory]], a '''large cardinal property''' is a certain kind of property of [[Transfinite number|transfinite]] [[cardinal number]]s. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than [[aleph zero|<math>\aleph_0</math>]], bigger than the [[cardinality of the continuum]], etc.). The proposition that such cardinals exist cannot be proved in the most common [[axiomatization]] of set theory, namely [[ZFC]], and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results. In other words, they can be seen, in [[Dana Scott]]'s phrase, as quantifying the fact "that if you want more you have to assume more".<ref>{{cite book|last=Bell|first=J.L.|title=Boolean-Valued Models and Independence Proofs in Set Theory|pages=viii|publisher=Oxford University Press|year=1985|isbn=0-19-853241-5|nopp=true}}</ref>


There is a rough convention that results provable from ZFC alone may be stated without hypotheses, but that if the proof requires other assumptions (such as the existence of large cardinals), these should be stated. Whether this is simply a linguistic convention, or something more, is a controversial point among distinct philosophical schools (see [[#Motivations and epistemic status|Motivations and epistemic status]] below).
L大電力動作、致命的な打撃と低温側へ [http://www.aseanacity.com/webalizer/prada-bags-27.html 財布 ブランド プラダ]。 ちょうど彼の呼吸から10以内に取りに言っ<br>サイド寒さが、彼はまた、単純に、はっきりと聞き、屈辱としてひざまずく、彼の怒り、そして冷たいキラー抑制の側へキャストする [http://www.aseanacity.com/webalizer/prada-bags-32.html プラダ 迷彩 財布]。<br>はきらびやかな剣のタイヤが彼の手にかかって動きを眉毛。 手に<br>真実剣タイヤグリップは、彼が天を見渡す、一般の人々を見下ろす、9日間、妖精の王の真実を把握上書きするようです [http://www.aseanacity.com/webalizer/prada-bags-30.html プラダ 財布]。 輝く彼の手のタイヤ、すべての光の中で<br>剣は、すべての世界が逆さまにすべての法律は、とにかくルアン割り当てられ、真実の暗い世界を照らしている [http://www.aseanacity.com/webalizer/prada-bags-22.html プラダ 財布 定価]。 彼の体は自然に、この瞬間、非斜め斜めのように、非陽性である、世界のアークを表すように、すべての人が彼と世界のラジアンを組み合わせることを感じ、フェンシング姿勢を形成<br> [http://www.aseanacity.com/webalizer/prada-bags-21.html プラダ 財布 スタッズ]。 世界そのものは感から押された<br>
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<ul>
 
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</ul>


A '''large cardinal axiom''' is an axiom stating that there exists a cardinal (or perhaps many of them) with some specified large cardinal property.
== dare disrespect for the elders too ==


There is no generally agreed precise definition of what a large cardinal property is, though essentially everyone agrees that those in the [[List of large cardinal properties]] are large cardinal properties.
Of an eternal giants, that should be broad to battle, [http://www.aseanacity.com/webalizer/prada-bags-29.html プラダ スタッズ 財布] give a feast to celebrate.<br>If an immortal character, then that would be heaven sue ancestors.<br>even more shocking is that Fang said he has begun to comprehend the cold of space law. What<br>comprehend [http://www.aseanacity.com/webalizer/prada-bags-29.html プラダ スタッズ 財布] space law is? The world has begun to contact the origin, the real monks do not [http://www.aseanacity.com/webalizer/prada-bags-30.html プラダ 財布] belong to the.<br>belong to legend, ancient, epic, all gorgeous adjectives, such a person who can ever accumulate.<br>original Xiu Hua days are immortal, shocking enough, and now the cold side, more [http://www.aseanacity.com/webalizer/prada-bags-22.html prada 新作 財布] shocking than him.<br>'Humph! side cold, what is your identity, even if it is your practice to immortality! do not get [http://www.aseanacity.com/webalizer/prada-bags-34.html プラダ 長財布] too much on the elders acknowledged that can never expect to become deputy head, so you're just a real disciple, dare we disrespectful.<br>dare disrespect for the elders too, as you are evil, you want anti-feathering out the door I not? Give me kneel
相关的主题文章：
<ul>
 
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</ul>


==Partial definition==
== for the yù for. ' ==
A necessary condition for a property of cardinal numbers to be a ''large cardinal property'' is that the existence of such a cardinal is not known to be inconsistent with [[ZFC]] and it has been proven that if ZFC is [[consistent]], then ZFC + "no such cardinal exists" is consistent.


==Hierarchy of consistency strength==
, Invincible, for the yù for. '<br>'Indeed, this treasure for us mén faction, has a [http://www.aseanacity.com/webalizer/prada-bags-22.html prada 新作 財布] crucial role.'<br>'We rush into which it into the xiǎo stone Huang, wind edge, Wu Pa, Chi boxing, who have shied away from.'<br>outside treasure everywhere Xianshu sound of the explosion, one after another, simply as blasting in general. Some wise sage, royal reincarnation, rushed into the hall in front of the space, tearing [http://www.aseanacity.com/webalizer/prada-bags-34.html prada] Buddha.<br>head is lonely family, the Rams family, a distant camp, too [http://www.aseanacity.com/webalizer/prada-bags-28.html prada 財布 2014] a mén ....... leaders of some of [http://www.aseanacity.com/webalizer/prada-bags-32.html プラダ ピンク 財布] the Son.<br>they just rushed mén mouth, suddenly, mén mouth out an invincible impact SG, earth-shattering explosion out, xiǎo Shi Huang, Wu Ba's body flew out, hit leader among this group of Son , the [http://www.aseanacity.com/webalizer/prada-bags-26.html 財布 プラダ レディース] current leader of several statues Son's body was directly torn, ripped, hair
A remarkable observation about large cardinal axioms is that they appear to occur in strict [[linear order]] by [[consistency strength]]. That is, no exception is known to the following: Given two large cardinal axioms A1 and A2, one of three things happens:
相关的主题文章：
#ZFC proves "ZFC+A1 is consistent if and only if ZFC+A2 is consistent";
<ul>
#ZFC+A1 proves that ZFC+A2 is consistent; or
 
#ZFC+A2 proves that ZFC+A1 is consistent.
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If it is discovered that two (or more) of these conditions hold, then all of them hold and ZFC+A1 is inconsistent and ZFC+A2 is inconsistent; in this case, these 'axioms' would no longer be considered large cardinal axioms.
 
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</ul>


In case 1 we say that A1 and A2 are [[Equiconsistency|equiconsistent]]. In case 2, we say that A1 is consistency-wise stronger than A2 (vice versa for case 3). If A2 is stronger than A1, then ZFC+A1 cannot prove A2 is consistent, even with the additional hypothesis that ZFC+A1 is itself consistent (provided of course that it really is). This follows from [[Gödel's second incompleteness theorem]].
== which is not necessarily genius Johnson sè ==


The observation that large cardinal axioms are linearly ordered by consistency strength is just that, an observation, not a theorem. (Without an accepted definition of large cardinal property, it is not subject to proof in the ordinary sense). Also, it is not known in every case which of the three cases holds. [[Saharon Shelah]] has asked, "[i]s there some theorem explaining this, or is our vision just more uniform than we realize?" [[W. Hugh Woodin|Woodin]], however, deduces this from the [[&Omega;-conjecture]], the main unsolved problem of his [[Ω-logic]].
You and I live dead, other mén sent the Son to see how? Let them have an opportunity. You know, the blood sè trials, [http://www.aseanacity.com/webalizer/prada-bags-29.html プラダ スタッズ 財布] we can be more than two, but there are hundreds Son. Especially Makino family, Huangfu family and other supreme big family, which is not necessarily [http://www.aseanacity.com/webalizer/prada-bags-27.html prada 財布 人気] genius Johnson sè, will not let that Songteng Fei inflating. '<br>side cold eloquent, careful thought, 'I'm just a bit projections, future Fun luàn, even with the situation in a rudderless seen many 宋腾飞 [http://www.aseanacity.com/webalizer/prada-bags-32.html プラダ 財布 リボン] trouble, a lot of people want beheaded him, we can not do first months. priority is to find the [http://www.aseanacity.com/webalizer/prada-bags-33.html prada] location where 宋腾飞 secretly observe and wait shot. '<br>'Well, which I also take into account blood sè [http://www.aseanacity.com/webalizer/prada-bags-33.html prada] Son of trial mén send too much, which also has supernatural powers of generation, and even to the ancient royal fairy reincarnation of real figures, such as Makino family, Huangfu family master, in addition, a large easy to teach, too, on nine Qing Tian
 
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It should also be noted that the order of consistency strength is not necessarily the same as the order of the size of the smallest witness to a large cardinal axiom. For example, the existence of a [[huge cardinal]] is much stronger, in terms of consistency strength, than the existence of a [[supercompact cardinal]], but assuming both exist, the first huge is smaller than the first supercompact.
<ul>
 
 
==Motivations and epistemic status==
  <li>[http://www.macha.jp/cgi-bin/bbs/light.cgi http://www.macha.jp/cgi-bin/bbs/light.cgi]</li>
Large cardinals are understood in the context of the [[von Neumann universe]] V, which is built up by [[transfinite induction|transfinitely iterating]] the [[powerset]] operation, which collects together all [[subset]]s of a given set. Typically, models in which large cardinal axioms ''fail'' can be seen in some natural way as submodels of those in which the axioms hold. For example, if there is an [[inaccessible cardinal]], then "cutting the universe off" at the height of the first such cardinal yields a [[universe (mathematics)|universe]] in which there is no inaccessible cardinal. Or if there is a [[measurable cardinal]], then iterating the ''definable'' powerset operation rather than the full one yields [[Gödel's constructible universe]], L, which does not satisfy the statement "there is a measurable cardinal" (even though it contains the measurable cardinal as an ordinal).
 
 
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Thus, from a certain point of view held by many set theorists (especially those inspired by the tradition of the [[Cabal (set theory)|Cabal]]), large cardinal axioms "say" that we are considering all the sets we're "supposed" to be considering, whereas their negations are "restrictive" and say that we're considering only some of those sets. Moreover the consequences of large cardinal axioms seem to fall into natural patterns (see Maddy, "Believing the Axioms, II"). For these reasons, such set theorists tend to consider large cardinal axioms to have a preferred status among extensions of ZFC, one not shared by axioms of less clear motivation (such as [[Martin's axiom]]) or others that they consider intuitively unlikely (such as [[V=L|V&nbsp;=&nbsp;L]]). The hardcore [[Philosophy of mathematics#Mathematical_realism|realists]] in this group would state, more simply, that large cardinal axioms are ''true''.
 
 
  <li>[http://tm1.math.uh.edu/search.cgi http://tm1.math.uh.edu/search.cgi]</li>
This point of view is by no means universal among set theorists. Some [[Philosophy of mathematics#Formalism|formalists]] would assert that standard set theory is by definition the study of the consequences of ZFC, and while they might not be opposed in principle to studying the consequences of other systems, they see no reason to single out large cardinals as preferred. There are also realists who deny that [[ontological maximalism]] is a proper motivation, and even believe that large cardinal axioms are false. And finally, there are some who deny that the negations of large cardinal axioms ''are'' restrictive, pointing out that (for example) there can be a [[transitive set|transitive]] set model in L that believes there exists a measurable cardinal, even though L itself does not satisfy that proposition.
 
 
</ul>
==Notes==
<references/>
 
==References==
* {{cite book|author=Drake, F. R.|title=Set Theory: An Introduction to Large Cardinals (Studies in Logic and the Foundations of Mathematics ; V. 76)|publisher=Elsevier Science Ltd|year=1974|isbn=0-444-10535-2}}
* {{cite book|author=Jech, Thomas|title=Set theory, third millennium edition (revised and expanded)|publisher=Springer|year=2002|isbn=3-540-44085-2|authorlink=Thomas Jech}}
* {{cite book|last=Kanamori|first=Akihiro|year=2003|authorlink=Akihiro Kanamori|publisher=Springer|title=The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings|edition=2nd|isbn=3-540-00384-3}}
*{{citation|last=Kanamori|first=Akihiro|first2=M. |last2=Magidor
|chapter=The evolution of large cardinal axioms in set theory
|series=Lecture Notes in Mathematics
|publisher =Springer Berlin / Heidelberg
|volume =669 ([http://math.bu.edu/people/aki/e.pdf typescript])
|title=Higher Set Theory
|year=1978
|isbn =978-3-540-08926-1
|doi =10.1007/BFb0103104
|pages=99–275
}}
* {{cite journal|last=Maddy|first=Penelope|title=Believing the Axioms, I|journal=Journal of Symbolic Logic|volume=53|issue=2|year=1988|pages=481–511|authorlink=Penelope Maddy|doi=10.2307/2274520}}
* {{cite journal|last=Maddy|first=Penelope|title=Believing the Axioms, II|journal=Journal of Symbolic Logic|volume=53|issue=3|year=1988|pages=736–764|doi=10.2307/2274569}}
* {{cite arxiv|last=Shelah|first=Saharon|title=The Future of Set Theory|year=2002|eprint=math/0211397|authorlink=Saharon Shelah}}
* {{cite journal|last=Solovay|first=Robert M.|coauthors=William N. Reinhardt, and [[Akihiro Kanamori]]|year=1978|title=Strong axioms of infinity and elementary embeddings|journal=Annals of Mathematical Logic|volume=13|issue=1|pages=73–116|authorlink=Robert M. Solovay|url=http://math.bu.edu/people/aki/d.pdf|doi=10.1016/0003-4843(78)90031-1}}
* {{cite journal|last=Woodin|first=W.Hugh|title=The continuum hypothesis, part II|journal=Notices of the American Mathematical Society|volume=48|issue=7|year=2001|pages=681–690}}
 
{{Set theory}}
[[Category:Large cardinals| ]]

Latest revision as of 13:17, 18 August 2014

 ちょうど彼の呼吸から10以内に取りに言っ

L大電力動作、致命的な打撃と低温側へ 財布 ブランド プラダ。 ちょうど彼の呼吸から10以内に取りに言っ
サイド寒さが、彼はまた、単純に、はっきりと聞き、屈辱としてひざまずく、彼の怒り、そして冷たいキラー抑制の側へキャストする プラダ 迷彩 財布。
はきらびやかな剣のタイヤが彼の手にかかって動きを眉毛。 手に
真実剣タイヤグリップは、彼が天を見渡す、一般の人々を見下ろす、9日間、妖精の王の真実を把握上書きするようです プラダ 財布。 輝く彼の手のタイヤ、すべての光の中で
剣は、すべての世界が逆さまにすべての法律は、とにかくルアン割り当てられ、真実の暗い世界を照らしている プラダ 財布 定価。 彼の体は自然に、この瞬間、非斜め斜めのように、非陽性である、世界のアークを表すように、すべての人が彼と世界のラジアンを組み合わせることを感じ、フェンシング姿勢を形成
プラダ 財布 スタッズ。 世界そのものは感から押された
相关的主题文章：

dare disrespect for the elders too

Of an eternal giants, that should be broad to battle, プラダ スタッズ 財布 give a feast to celebrate.
If an immortal character, then that would be heaven sue ancestors.
even more shocking is that Fang said he has begun to comprehend the cold of space law. What
comprehend プラダ スタッズ 財布 space law is? The world has begun to contact the origin, the real monks do not プラダ 財布 belong to the.
belong to legend, ancient, epic, all gorgeous adjectives, such a person who can ever accumulate.
original Xiu Hua days are immortal, shocking enough, and now the cold side, more prada 新作 財布 shocking than him.
'Humph! side cold, what is your identity, even if it is your practice to immortality! do not get プラダ 長財布 too much on the elders acknowledged that can never expect to become deputy head, so you're just a real disciple, dare we disrespectful.
dare disrespect for the elders too, as you are evil, you want anti-feathering out the door I not? Give me kneel 相关的主题文章：

for the yù for. '

, Invincible, for the yù for. '
'Indeed, this treasure for us mén faction, has a prada 新作 財布 crucial role.'
'We rush into which it into the xiǎo stone Huang, wind edge, Wu Pa, Chi boxing, who have shied away from.'
outside treasure everywhere Xianshu sound of the explosion, one after another, simply as blasting in general. Some wise sage, royal reincarnation, rushed into the hall in front of the space, tearing prada Buddha.
head is lonely family, the Rams family, a distant camp, too prada 財布 2014 a mén ....... leaders of some of プラダ ピンク 財布 the Son.
they just rushed mén mouth, suddenly, mén mouth out an invincible impact SG, earth-shattering explosion out, xiǎo Shi Huang, Wu Ba's body flew out, hit leader among this group of Son , the 財布 プラダ レディース current leader of several statues Son's body was directly torn, ripped, hair 相关的主题文章：

which is not necessarily genius Johnson sè

You and I live dead, other mén sent the Son to see how? Let them have an opportunity. You know, the blood sè trials, プラダ スタッズ 財布 we can be more than two, but there are hundreds Son. Especially Makino family, Huangfu family and other supreme big family, which is not necessarily prada 財布 人気 genius Johnson sè, will not let that Songteng Fei inflating. '
side cold eloquent, careful thought, 'I'm just a bit projections, future Fun luàn, even with the situation in a rudderless seen many 宋腾飞 プラダ 財布 リボン trouble, a lot of people want beheaded him, we can not do first months. priority is to find the prada location where 宋腾飞 secretly observe and wait shot. '
'Well, which I also take into account blood sè prada Son of trial mén send too much, which also has supernatural powers of generation, and even to the ancient royal fairy reincarnation of real figures, such as Makino family, Huangfu family master, in addition, a large easy to teach, too, on nine Qing Tian 相关的主题文章：

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