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In 1938 Gödel published “The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis”. This paper introduces the constructible universe, a so-called inner model of ZFC. This is a class L that satisfies the ZFC axioms, plus GCH, provided that V satisfies the ZF axioms. So if ZF is consistent, then so is ZF+AC+GCH. Continue reading →

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The Mysterium cosmographicum

The Mysterium cosmographicum (Cosmographical Mystery) boasts one of most celebrated illustrations in the history of science: the planetary spheres nested with the five Platonic solids. This picture graces nearly every history of astronomy. Who am I to break with tradition, here it is: Continue reading →