The axioms ZFC do not provide a concise conception of the Universe of Sets. This claim has been well documented in the 50 years since Paul Cohen established that the problem of the Continuum Hypothesis cannot be solved on the basis of these axioms. Godel's Axiom of Constructibility, V = L, provides a conception of the Universe of Sets which is perfectly concise modulo only large cardinal axioms which are strong axioms of infinity. However the axiom V = L limits the large cardinal axioms which can hold and so the axiom is false. The Inner Model Program which seeks generalizations which are compatible with large cardinal axioms has been extremely successful, but incremental, and therefore by its very nature unable to yield an ultimate enlargement of L. The situation has now changed dramatically and there is, for the first time, a genuine prospect for the construction of an ultimate enlargement of L.
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机译：Axioms ZFC不提供套装宇宙的简洁构想。这一索赔在50年来凭借Paul Cohen确定的是，在这些公理的基础上无法解决连续假设的问题。戈德尔的结构性v = L，提供了宇宙宇宙的构想，这是完全简洁的模数，这只是较大的无限公理的大型基本公理。然而，Axiom V = L限制了可以保持的大型基本轴理，因此公理是假的。寻求与大型基本公理兼容的概括的内模拟程序非常成功，但增量，因此，其本质上无法产生L的最终扩大。情况现在发生了巨大变化，而且第一个情况时间，建设L.终极扩大的真正前景。
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