Date: Aug 16, 2013 4:54 AM
Author: Peter Percival
Subject: Can addition be defined in terms of multiplication?

Can addition be defined in terms of multiplication?  I.e., is there a 
formula in the language of arithmetic

x + y = z <-> ...

such that in '...' any of the symbols of arithmetic except + may occur?
Or, alternatively, is there a formula in the language of arithmetic

x + y = ...

with the same requirement?

The symbols of arithmetic (for the purpose of this question) are either

individual variables, (classical) logical constants including =,
S, +, *, and punctuation marks;

or the above with < as an additional binary predicate symbol.

--
Sorrow in all lands, and grievous omens.
Great anger in the dragon of the hills,
And silent now the earth's green oracles
That will not speak again of innocence.
David Sutton -- Geomancies