[FOM] FIRST-ORDER LOGIC WITH IDENTITY, INDIVIDUAL CONSTANTS AND FUNCTION CONSTANTS.

[A.P. Hazen]

John Corcoran asks various questions  about the history of the logic 
mentinoned in the title.  I'm not sure who would have formulated the 
theory of individual constants and function-symbols  explicitly 
(their theoretical dispensability is a consequence of Russell's 
theory of descriptions and would have been familiar to foundational 
workers of the 1920s), but Gödel DOES discuss identity in his 1930 
completeness theorem paper: theorems VII and VIII state weak 
completeness (= valid formulas provable) for FOL-with-identity, and 
after giving theorems IX (strong completeness (a contradiction is 
derivable from any denumerable set of formulas which is not 
satisfiable)) and X (Compactness) for FOL, Gödel remarks that they 
also generalize to FOL-with-I.

Allen Hazen
Philosophy Department
University of Melbourne

Corcoran's questions:
>1 Who discusses the history of this logic?
>2 Who were the early logicians to specifically mention this logic as an
>extension of Gödel 1930 logic?
>3 Who were the early logicians to notice that the Gödel 1930
>completeness results extend to this logic?
>43 Who were the early logicians to formulate the semantics and actually
>carry out a completeness proof?