# The LargeCardinalHierarchy package

[ Tags: library, math, mathematics, maths, set-theory ] [ Propose Tags ]

## Properties

Versions 0.0.0, 0.0.1 base (>=2 && <4) [details] OtherLicense Copyright (c) 2010 Stephen E. A. Britton Stephen E. A. Britton Stephen E. A. Britton Math, Maths, Mathematics, Set Theory Sun Sep 7 19:14:56 UTC 2014 by Stephen_E_A_Britton NixOS:0.0.1 862 total (27 in the last 30 days) (no votes yet) [estimated by rule of succession] λ λ λ Docs not available All reported builds failed as of 2016-10-25 Hackage Matrix CI

## Modules

• LargeCardinalHierarchy

Copyright (c) 2010 Stephen E. A. Britton.
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).