Alessandro Padoa

Alessandro Padoa (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms.
The following description of Padoa's career is included in a biography of Peano:
The congresses in Paris in 1900 were particularly notable. Padoa's addresses at these congresses have been well remembered for their clear and unconfused exposition of the modern axiomatic method in mathematics. In fact, he is said to be "the first … to get all the ideas concerning defined and undefined concepts completely straight".
Congressional addresses.
Philosophers' congress.
At the International Congress of Philosophy Padoa spoke on "Logical Introduction to Any Deductive Theory". He says
Padoa went on to say:
Mathematicians' congress.
Padoa spoke at the 1900 International Congress of Mathematicians with his title "A New System of Definitions for Euclidean Geometry". At the outset he discusses the various selections of primitive notions in geometry at the time:
Padoa completed his address by suggesting and demonstrating his own development of geometric concepts. In particular, he showed how he and Pieri define a line in terms of 
collinear points.
Bibliography.
Secondary: