[FOM] The Patterns of Resemblance Ordinal Calculator

Alexander, Samuel alexander at math.ohio-state.edu
Fri Dec 7 18:18:49 EST 2012

I am very happy to announce the official opening of the Patterns of Resemblance Ordinal Calculator.


The POR Ordinal Calculator does arithmetic on ordinals below the ordinal of Pi^1_1-CA_0, notated using first-order additive Patterns of Resemblance, a beautiful combinatorial notation system discovered by Timothy J. Carlson.

Currently implemented operations are addition, comparison, multiplication, and base-omega exponentiation and logarithm.  Future operations (epsilon, Veblen, etc.) are planned.

The calculator requires no download or installation.  It works on any computer with an internet connection and a modern browser (including smartphones and tablets).  Notations generated by the calculator come with unique, permanent, public IDs which can be used to easily share patterns with other researchers or simply return to your own calculations at a later time.

A few samples:
The ordinal epsilon_0: http://www.xamuel.com/patterns/du/
The ordinal Gamma_0: http://www.xamuel.com/patterns/dy/
The Howard-Bachmann ordinal: http://www.xamuel.com/patterns/jz/
Suppose you want to calculate the product Gamma_0 * epsilon_0.  Simply enter the command: mult dy du

The calculator has an interactive tutorial which can be started by entering the command, "tutorial".

I hope you will find the calculator fun and useful.

-Samuel Alexander
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