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The real reach of the constructible universe

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The universe L of constructible sets is a class model of ZFC , the Generalized Continuum Hypothesis, Diamond, and the Axiom of Constructibility V = L. It is the minimal inner model of set theory within an ambient universe V. Yet despite this minimality property, and the possibility of non-constructible reals in V, every real number is an element of a model of ZFC + V = L. The talk will introduce L, its definition and basic properties, and sketch the proof that its reach can and does exceed its grasp in the manner described.

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