> 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?
x + y = log(e^x * e^y)
> 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. >