                                OrdCalc
        An interactive tool to understand the recursive ordinals

'ord' is a program for understanding the recursive ordinals.
It has a command line interpreter resembling command line calculators.
See 'ordCalc.pdf' for a description of how to use the interpreter.
See 'ordinal.pdf' for a description of the structure of the program and the
theory on which it is based.

This project is licensed for use and distribution under the terms
of the GNU GENERAL PUBLIC LICENSE, Version 2, June 1991. See file COPYING for
complete information. Users are encouraged to extend the capabilities of this
program and distribute it under the terms of this license.

DOWNLOAD LOCATIONS:

http://www.mtnmath.com/ord
https://sourceforge.net/projects/ord

OTHER VERSIONS:

In addition to the source code version that should
build on many Linux and other Unix computers.
there is a prebuilt Microsoft Windows installation
available. That version is built with CYGWIN. Different
releases of CYGWIN may use different incompatible versions of
'cygwin1.dll'. Only one version of a 'dll' file can be in
use at the same time. Thus you may not be able to run 'ord'
while running other CYGWIN tools and vice versa.

REQUIREMENTS:

To build 'ord' you must have The GNU MP Bignum library including the C++
library installed. You may be able to do this with "yum install gmp".  This
package is also available at "gmplib.org".

You also need the GNU 'readline' library. You may be able to do:
"yum install readline". If not, you can get the library at:
"gnuwin32.sourceforge.net/packages/readline.htm".

INSTALLATION:

To build the program on most Linux and many other Unix based
platforms type 'make' in this directory. The output is file 'ord'
in subdirectory 'src' and a series of tests to validate the installation.
There should be a log of test results in src/test.log

To run these tests again type 'make TEST' in this directory or 'src'. 

BUILDING DOCUMENTATION:

To build the program and documentation type 'make ALL' in this directory.
There should be a prebuilt version of the documentation (ordinal.pdf and
ordCalc.pdf) in this directory. There is no need to build them unless
you edit the documentation.

A portion of the documentation is created by program 'ord' and it must
be built first. You need to have a fairly complete TeX/LaTeX installation to
build the documentation. To do so type 'make DOC' in this top level directory.

LONG TERM AIM:

In addition to serving as a tutorial tool to understand the recursive
ordinals, this is intended as a possible basis for extending the ordinal
hierarchy and thus the power of mathematics. It is, in theory, possible
to define a recursive ordinal strong enough to prove the consistency of
Zermelo-Frankel set theory and go way beyond this, but the complexity of
the structures required soon becomes overwhelming. Computer Science has,
over the decades, learned a great deal about dealing with overwhelming
complexity. Applying these techniques to the foundations of mathematics
may allow significant extensions of that discipline. However, the
indirect approach, that must be used, is alien to the philosophy of
mathematics that wants direct human understanding of all proofs.

