[FOM] Axioms for ordinal addition

[MartDowd at aol.com]

Does anyone know of a reference giving a set of axioms for ordinal  
addition, in the language 0,1,+,<?  It seems both + and < are needed;  for example 
Lim(alpha) is beta<alpha => beta+1<alpha.  There's a  more or less obvious 
system, but getting the details right is a bit tricky and  it would be 
helpful to check it against an existing reference.
 
- Martin Dowd
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