Mathematical Sciences: The Definable Continuum Hypothesis

此时，我们知道，有许多命题， 与Zermelo-Frankel公理无关的数学 集合论 其中最重要的是连续统假设。 这使得研究人员提出了更强的公理，称为 大基数公理试图解决这些问题。 教授 福尔曼计划研究的强公理的关系 连续统假设的集合论。 特别是他 证明普通的大基数公理应该意味着， 没有可定义的或可构造的反例， 连续统假说 他已经证明了大量的部分结果 并计划继续研究这一猜想。 这种调查触及到最基本的基础， 数学，澄清我们对无限的理解。

At this time it is known that there are many propositions of mathematics independent of the ordinary axioms of Zermelo-Frankel set theory. Foremost among these is the continuum hypothesis. This has led investigators to pose stronger axioms, known as large cardinal axioms to try to settle these problems. Professor Foreman plans to investigate the relationship of strong axioms of set theory to the continuum hypothesis. In particular he conjectures that ordinary large cardinal axioms should imply that there are no definable or constructable counterexamples to the continuum hypothesis. He has proven substantial partial results in this direction and plans to continue work on this conjecture. Such investigations reach to the most basic foundations of mathematics, clarifying our understanding of the infinite.