The LargeCardinalHierarchy package

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Versions 0.0.0, 0.0.1
Dependencies base (>=2 && <4) [details]
License OtherLicense
Copyright Copyright (c) 2010 Stephen E. A. Britton
Author Stephen E. A. Britton
Maintainer Stephen E. A. Britton
Category Math, Maths, Mathematics, Set Theory
Uploaded Sun Sep 7 19:14:56 UTC 2014 by Stephen_E_A_Britton
Distributions NixOS:0.0.1
Downloads 552 total (20 in the last 30 days)
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Status Docs not available [build log]
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  • LargeCardinalHierarchy

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Readme for LargeCardinalHierarchy

Readme for LargeCardinalHierarchy-0.0.1

Copyright (c) 2010 Stephen E. A. Britton.
All rights reserved.

The LargeCardinalHierarchy module defines a recursively enumerable, countably infinite subclass of the logically (consistent) maximal transfinite set-theoretic universe ZFC+Con(LargeCardinals) (Zermelo-Frankel Set Theory + Axiom of Choice + All known large cardinals consistent with ZFC) via data constructors for each large cardinal within the hierarchy and functions over them. The algebraic data type Card is a Haskell implementation of the set theoretic proper class of all cardinals, Card. Card has value constructors for a countably infinite (aleph-null sized) subset of every cardinal type of all known large cardinals consistent with ZFC (Zermelo-Frankel Set Theory + Axiom of Choice) or, equivalently, ZF+GCH (Zermelo-Frankel Set Theory + Generalized Continuum Hypothesis).