In an incense burner, several light smokes wind around. In the entire room cannot see any light source, but does not know from where comes light/only, room illuminates every inchs. The good large xuan paper is on record the neat code. The master by chance soft pen of library, therefore on the desk also has a side inkslab. In the inkstone has black ink, even viscous, resembling is the oil resembles is the water. A writing brush is away from. 一尊香炉之中,几丝青烟缭绕。整间屋子里看不到任何光源,但是不知从何而来的光,就是将房间的每一寸都照亮。上好的大幅宣纸在案上齐齐整整的码着。书斋的主人更加偏好软笔,因此书桌上还有一方砚台。砚中有墨,均匀粘稠,似是油又似是水。一杆毛笔隔着。 These black ink, as if are waiting, wait to turn into shocking article the moment. 那些墨,仿佛在等待,等待着自己变成惊世文章的一刻。 But in fact, these black ink resemble the new grinding, is only the magic arts effect on the inkslab bringing. That pen, has not moved for a long time. 可实际上,这些墨似新磨,也只是砚台上自带的法术效果。那杆笔,已经许久未动了。 The master of black ink and pen, stiff here for a long time. 墨与笔的主人,已经僵在这里好久了。 Calculates that lord clear, regardless of writes what character, will be presented as the treasured painting outside. Although his character truly is excellent. However, his status is the true side is high. 算主希柏澈,无论写什么字,在外面都都会被奉为墨宝。虽然他的字确实是极好。但是,他的身份才是真正的极高。 But, such a Deity, there is one day with a worried look. 可是,这样一位神人,也有愁眉不展的一日。 „Oh...... has not progressed.” He shakes the head, in the middle of the tranquil distant look, has the anxiety of not being able to conceal. “唉……还是没有进展。”他摇摇头,宁静悠远的眼神当中,有着掩饰不住的焦虑。 These days, he used oneself all. The achievement cannot say does not have, however is not worth mentioning. Compared with his own lofty aspirations and high ideals is really tiny. 这些日子,他倾尽了自己的一切。成果也不能说没有,但是不值一提。与他自己的雄心壮志相比实在是渺小。 Behind „teacher......” one of the clear disciples worries in him looks: „You probably were extremely recently anxious......” “老师……”希柏澈的弟子之一在他身后担忧的看着:“最近您好像太过忧虑了……” „Yes.” Calculates the Lord deep sigh: „Is Monarch...... only the theory calculates saying that certainly the one who does not have the anti- hand is Mr . Such character kills, if I did not fear, that side was not my.” “是啊。”算主长叹:“算君啊……仅论算道,绝无抗手的算君。这样的人物杀过来,我若不怕,那边不是我的了。” Calculates that Lord non- is the talent. Discussed by the words of peer, he was „diligently class talent”, to cultivate/repair to hold itself assiduously, relentless., Among his of the same generation talent, has fallen on his behind naturally. 算主非是天才。以同辈的话而论,他是“努力类的天才”,以勤勉修持自身,坚持不懈。自然而然的,他同辈当中的天才,就已落在了他的后面。 His life, has to defeat, has not feared. Therefore, he does not shame in discussing these...... 他这一生,并非没有败过、没有怕过。因此,他也不羞于谈论这些…… Naturally, thinks that anything said anything. 自然而然,想到什么就说什么。 „Teacher, you could to such rest in the past, relax. The complete law, cannot attack and capture actually may not. You looked, 35 years ago we have proven the completeness of arithmetic many extensive system......” “老师,您或许可以向往常那样休息休息,散散心。完备律这一关,其实并非非得攻克不可。您看,三五年前我们已经证出了算学不少分支系统的完备性……” „what branch.” Name that clear was called this student: „What news did you hear recently?” “何科。”希柏澈一口叫出这个学生的名字:“你最近是不是听到了什么消息？” This half free member, is one of his earlier several disciples. The sentiment with calculating the Lord afterward disciple was different. His some do not dare to look the back of own teacher, lowers the head saying: „Recently...... I and Junior Brother what have contacted......” 这位半步逍遥的修士,乃是他早年的几位弟子之一。感情与算主后来的弟子自是不一样。他有些不敢去看自己老师的背影,低头道:“最近……我和何师弟接触过了……” What outside is calculates that Lord has the disciple of achievement. Calculates that the Lord many disciples politely call him for the Senior Brother. However what branch type older, then calls it the Junior Brother. 何外尔是算主就有成就的弟子。算主的不少弟子都尊称他为师兄。但是何科这种更加年长的,则称之为师弟。 clear showed the having a headache expression: „After outside...... that fellow letter/believed the even/including sect, changed. What did he say?” 希柏澈露出了头疼的表情:“外尔啊……那家伙信了连宗之后,就变了。他说什么了？” „I have searched his rumor very not wonderfully, matter as if really......” “我探过他的口风,事情似乎真的很不妙……” „Seemingly calculates some Monarch skills.” Calculates that the principal point nods. Thinking little: „The loophole of my theory are many, if he can help me discover a difference/two kinds, I am deeply grateful actually. Just, should he disdain in pondering this domain? Snort.” “看起来算君还是有些本事的。”算主点点头。不以为意:“我理论的漏洞很多,他若是能够帮我找出一两样,我倒是感激不尽。只不过,他应该不屑于思考这个领域吧？哼。” what branch clenches teeth: „Also, Mr. Feng...... Mr. Feng also knows. They worried that you cannot support......” 何科咬咬牙:“还有,冯先生……冯先生也知道。只是,他们都担心您挺不过去……” „How I said my old friend stealthily recently, originally this?” clear expression was somewhat dignified: „Seeming like, is really the major problem. Can have many foundation? Where I am......” “我说我这老朋友最近怎么鬼鬼祟祟的,原来这这样吧？”希柏澈表情有些凝重了:“看起来,真的是大问题啊。能有多基础呢？我到底是哪里……” In what Kexin an icy coldness: By the present, the mentality of teacher on has not depended on the completeness that...... he does not suspect the arithmetic toward „completeness”...... 何科心中一片冰凉:到现在,老师的思路都没有往“完备性”上靠……他根本不怀疑算学的完备性…… „Teacher, we have the escape route. We can adopt the ultra poor induction. The completeness of proof system from system......” “老师,我们还有退路的。我们还是能够通过超穷归纳法。从系统外证明系统的完备性……” what branch had not said that is too long. Calculates that the Lord eye is staring at him. That black pupil as if whether there is side boldness. Quick, he could not be justified. Crossed some little time, calculates that Lord pulled back that to stagnate for a long time proof the vision. He as if wants along this certificate, „sees” the other shore of arithmetic. 何科没有说太久。算主的眼睛盯着他。那黑色的眸子似乎有无边的魄力。很快,他就说不下去了。过了好一会,算主才将目光拉回到那个自己已经停滞了许久的证明。他仿佛想要沿着这个证明,“看到”算学的彼岸。 „We must know, we will certainly know......” “我们必须知道,我们必将知道……” He in a soft voice twittering. 他轻声呢喃。 „In brief, my recent mentality.” king Qi a face light was reporting own mentality to Feng Luoyi. “总而言之,我最近的思路了。”王崎一脸平淡的对着冯落衣汇报了自己的思路。 So-called „mentality”, needs to cover-up sometimes, but said sometimes might also as well. 所谓的“思路”,有些时候是需要藏着掖着,但是有些时候说出来也无妨。 king Qi the mentality regarding Feng Luoyi, is this. 王崎的这个思路对于冯落衣来说,就是这样。 Feng Luoyi is the member who the summit withstand/top. Regardless of the life benefits, he not higher request. This calculates in the family/home heart to think greatly. Nothing but obtains the main road, in addition has gets rid of that so-called „ultimate prospect”. In addition, had no benefit to touch him again. 冯落衣已经是巅顶的修士了。无论命还是利,他都没有更高的要求了。这位大算家心中所想的。无非就是求得大道,另外还有摆脱那个所谓的“终极图景”。除此之外,再也没有什么利益能够打动他了。 Rather, to realize his ideal. king Qi this talented later generation the more better. From this level, Feng Luoyi the support to king Zaki it can be said that spares no effort seriously. 倒不如说,为了实现他的理想。王崎这种有天分的后辈越多越好。从这个层面来讲,冯落衣对王崎的支持当真可以说是不遗余力。 This is also these already „reaching” the fellow is not parsimonious in leading by the hand the reason of later generation. 这也是那些已经“登顶”的家伙不吝啬于提携后辈的原因。 Feng Luoyi ponders king Qi the mentality in the mind. He thinks: „Looks at your situation, seems must kill to put on this unexpectedly 23 to ask.” 冯落衣则在脑海当中思考王崎的思路。他想到:“看你这态势,竟好似要杀穿这个二十三问啊。” „Does not dare, does not dare.” king Qi wants. Did 23 ask how fearfully? Even in Earth, in the middle of these 23 issues have several to ask that as before is unresolved. Even if he some confidence independent solutions 12 asked, does not dare to say can solve all. “不敢,不敢。”王崎要要有。二十三问何其可怕？就算在地球,这二十三个问题当中依旧有数问是悬而未决的。他就算有信心独立解决其中的一两问,也不敢说能够解决所有。 Feng Luoyi shakes the head: „Later matter. Who knows? 56 years ago, I have not looked, you can follow that completeness unexpectedly, penetrates second to ask at one fell swoop, tenth does not ask, perhaps must add first to ask again.” 冯落衣摇摇头:“以后的事情。谁知道呢？五六年前吧,我就没看出来,你居然能够循着那个完备性,一举击穿第二问、第十问唔,说不定还要再添上第一问。” „......” Feng Luoyi look is suddenly sharp: „You always like detouring probably very much.” “不过……”冯落衣的眼神突然锐利起来:“你好像总是很喜欢走弯路。” „Tortuous path?” “弯路？” king Qi is stunned. The forcing method is the perfect solution continual series supposition issue not two electing? Why is the tortuous path? 王崎错愕。力迫法才是完美解决连续统假设问题的不二之选啊？为什么是弯路？ „I saw a mentality recently, is very unusual, is very interesting.” Feng Luoyi is staring at king Qi the eyes, said: „All may establish the set with and becomes a system, quite infinite size in infinite......” “我最近看到了一个思路,很奇特,很有趣。”冯落衣盯着王崎的眼睛,道:“将所有可建立集合同和成一个系统,在无限中比较无限的大小……” king Qi is stunned: „Do some people want to come out?” 王崎错愕:“有人想出来了？” This was initially the approach of Goodall certificate continual series supposition! 这就是当初哥德尔证明连续统假设的思路！ In the range that in the zf axiom permits does to advance, showed that if the zf axiom-system has the uniformity, then continual series supposition for. In the zf axiomatics, the continual series supposed that is unable to be attested to falsity. 在zf公理允许的范围之内作推到,证明,若是zf公理系统具备一致性,则连续统假设为真。在zf公理体系之内,连续统假设无法被证伪。 regarding 23 asked that this should be a perfect answer. 对于二十三问来说,这应该已经算是一个完美的答案了。 However, „cannot attest to falsity” does not represent „confirmation”. 但是,“不能证伪”并不代表“证实”。 Along this mentality, people can prove similarly, in the zf axiom-system, the continual series supposition is unverifiable. 沿着这个思路,人们同样可以证出,在zf公理系统之内,连续统假设不能证实。 In other words, the continual series issue in the category of set theory, was one had the undecidability issue. If this „cannot confirm cannot attest to falsity of” conclusion again early, then does not need to show strictly tenth asked that this is to „decidability” an absolute counter-example. 换句话说,连续统问题在集合论的范畴之内,是一个具备了不可判定性的问题。如果这个“不能证实也不能证伪”的结论再早一点,那么不用严格证明第十问,这就是对“可判定性”的一个绝对反例。 Only then beyond the existing axiomatics, can show. 只有在现有公理体系之外,才能证明。 The forcing method, runs out of the fetter of original axiomatics, from opening the system, decides the path. 力迫法,就是冲出原有公理体系的束缚,自开体系、自定道路。 However, if tries the set theory and existing axiom-system is the cornerstone, then this „homemade” system, how should also calculate? Beside cornerstone? In arithmetic? 但是,若试集合论、现有公理系统为基石,那么这个“自创”的系统,又应该怎么算？基石之外？算学之内？ This is also the origin of forcing method great significance. 这也是力迫法重大意义的来源。 Hears king Qi calling out in alarm, Feng Luoyi vision flashes: „This mentality, have you also thought?” 听到王崎的惊呼,冯落衣眼光一闪:“这个思路,你也想到过是吧？” „Has thought indistinctly, but...... does not like greatly.” king Qi can only say. If by the concise and smooth degree of theory discussion process, Cohen's forcing method is well below Goodall's mentality. Only if were silly were insane, otherwise the average people will not rush out this road in the front sometimes. “隐约想到过,但是……不大喜欢。”王崎只能这么说了。若论理论论证过程的简明、流畅程度,科恩的力迫法远远不及哥德尔的思路。除非是傻了疯了,不然一般人都不会在前方还有的时候去闯出这条路的。 „Also does not have the basis ‚intuition’?” Feng Luoyi shakes the head, rare has not reproven king Qi, but sighed: „Before for several years, as if also had this matter...... you to avoid the average person to think that the normal path, took ‚dishonest means’, by ejected not the entire law few days ago, broke that completely reading, I discovered, long journey that originally you several years ago circled, was the only right way.” “又是没有根据的‘直觉’？”冯落衣摇摇头,罕见的没有训斥王崎,只是感叹:“数年之前,似乎也发生过这种事啊……你避开了一般人觉得正常的道路,走了‘歪路’,直到前些日子里抛出不全之律,破了那完全之念,我才发现,原来你前几年绕的远路,才是唯一的正路。” Feng Luoyi refers, is king Qi obtains around enjoying, with the unrestricted induction proves the arithmetic system uniform path. According to the average person thinks, he should „be complete according to predicate logic of first-order system that” oneself prove, from first-order pushes to high rank. 冯落衣所指的,乃是王崎获得道种赏前后,用超限归纳法证明算术系统一致性的道路。按照一般人所想,他应该根据自己证明的“一阶谓词逻辑系统完备”出发,从一阶推向高阶。 However, king Qi chose at that time, is proof system of an incomparably far road in beyond the system is not contradictory. 但是,王崎当时选择的,却是一条无比远的路在系统外证明系统内无矛盾。 The people will feel strange, the exceedingly high level roads, you do not walk obviously, must circle to the system beyond, isn't this silly? 众人会奇怪,明明有一条通天坦途,你偏不走,非要到系统外绕一圈,这不是傻吗？ At that time, only then king Qi understands, this system could not achieve „not false outside asks”. That that he circles, must. 当时,只有王崎明白,这个系统是做不到“不假外求”的。他绕的那一圈,才是必须的。 However, these time was not same. Goodall's that proof line, but does not have forcing method such significance to be big, without forcing method such indisputable effort. In fact, this as before is a right way. 不过,这一次就不大一样了。哥德尔的那个证明思路,只不过没有力迫法那样意义大,没有力迫法那样无可辩驳的力度。实际上,这依旧是一条正路。 He can only say: Issue that „this...... really likes personally. That mentality, must not wrong.” 他只能说道:“这……真的只是个人喜好的问题。那个思路,应当是没有错的。” „.” Feng Luoyi nods, does not know that has listened. “哦。”冯落衣点点头,也不知听没听进去。 „Right, Teacher.” king Qi somewhat was suddenly curious: „Is the starter of that mentality, who?” “对了,老师。”王崎突然有些好奇了:“那个思路的提出者,到底是谁？” Can the rare and beautiful flowers where comes, unexpectedly the independent thinking and Goodall big god exactly the same mentality of? 到底是哪来的奇葩,居然可以独立思考出和哥德尔大神一模一样的思路？ Feng Luoyi said with a smile: „You should also know. Ten thousand method true lines, Su Jun yu.” 冯落衣笑道:“你应该也认识。万法门真传,苏君宇。” „Senior Brother Su? His domain including logic?” king Qi is stunned. “苏师兄？他的领域包括逻辑吗？”王崎错愕。 The domain that in the middle of the impression, Su Jun yu that fellow studies is mixed, probably what has, is mainly the probability and how much...... the volume, words that wants to come, does he have contact logic possibility probably? If his day brain pulled out runs to study the logic to have the possibility! 印象当中,苏君宇那个家伙学习的领域非常杂,好像是什么都有,主要是概率和几何……额,这么想来的话,他好像也不是没有接触逻辑这一块的可能性啊？如果他那一天脑子一抽跑去学习逻辑非常有可能嘛！ However, this also is really the place of marvelous superposition. king Qi thinks: Initiator Cohen of forcing method, the research area is not the arithmetic logic. He most starts to first to ask purely is interested, therefore wants the cross domain to mix a foot. He cannot understand the forcing method actually the tremendous significance. 不过,这还真是奇妙的重合之处啊。王崎想到:力迫法的创始者科恩,研究领域就不是算学逻辑。他最开始只是单纯对第一问感兴趣,所以想要跨领域去掺一脚。他本人其实不能理解力迫法的巨大意义。 Su Jun yu estimated also thinks like this...... wants to mix a foot in the domain that first asked that finally this leg mixed the great achievement.( To be continued.) 苏君宇估计也是这样想的吧……想要在第一问的领域掺一脚,结果这一腿掺出了大成就。(未完待续。) ps: In Carvin the qaq mobile phone user please visit http://m.piaotian.net as before ps:依旧卡文中qaq手机用户请访问http://m.piaotian.net