Example 4

Tag 03V8, permanent. Cite it as [Bourbaki, Tag 03V8].

Theory of Sets, chapter IV, § 1. Structures and isomorphisms

\* Take $\mathscr{T}$ to be the theory of the species of division ring structures, which has (among other things) a constant K as unique (principal) base set. The species of structure of a left vector space over K has K as auxiliary base set, a principal base set E, and as typical characterization the relation

V \in \mathfrak{P}((E \times E) \times E) \times \mathfrak{P}((K \times E) \times E)

(pr $_1$ V being the graph of addition in E, and pr $_2$ V the graph of scalar multiplication); we shall not state here the axiom for this species of structures.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Remark 1, § 1

Cites

Nothing.