An overview of the ordinal calculator
Paul Budnik · 2012
An ordinal calculator has been developed as an aid for understanding the countable ordinal hierarchy and as a research tool that may eventually help to expand it. A GPL licensed version is available in C++. It is an interactive command line calculator and can be used as a library. It includes notations for the ordinals uniquely expressible in Cantor normal form, the Veblen hierarchies and a form of ordinal projection or collapsing using notations for countable admissible ordinals and their limits. The calculator does addition, multiplication and exponentiation on ordinal notations. For a recursive limit ordinal notation, α, it can list an initial segment of an infinite sequence of notations such that the union of the ordinals represented by the sequence is the ordinal represented by α. It can give the relative size of any two notations and it determines a unique notation for every ordinal represented. Input is in plain text. Output can be plain text and/or L ATEX math mode format. This approach is motivated by a philosophy of mathematical truth that sees objectively true mathematics as connected to properties of recursive processes. It suggests that computers are an essential adjunct to human intuition for extending the combinatorially complex parts of objective mathematics.