Σ * Fine Structure

Fine Structure is the name given to an analysis developed by Ronald Jensen in the late 60’s and early 70’s of Godel’s universe L of constructible sets with which Godel showed the consistency of the Axiom of Choice and Continuum Hypothesis with the usual axioms of set theory. As the name implies, the ramified nature of L that Godel used, is given a microscopic treatment of how sets are constructed. Jensen sought to replace the Godel levels L α with levels J α which are closed under certain rudimentary set functions and so are more useful for this purpose. This analysis turned out to be extremely fruitful and resulted in a wealth of information about the ordinal combinatorial structure of L, but moreover gave insight into a wealth of absolute facts about V the universe of all sets of mathematical discourse.

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