Who first proved that the second-order theory of real numbers is categorical?

logic math-history real-numbers foundations higher-order-logic

In his Set Theory book, Jech appropriates this theorem (Theorem 4.2 in the 2006 edition) to Cantor.

It should be worth linking to MacTutor which has a nice overview of the modern history of the real numbers.

Related

Intermediate fields of cyclotomic splitting fields and the polynomials they split
Find the number of $n$ husband's placing
Consequence of Nakayama Lemma's to Local Rings
Find all positive integers satisfying: $x^5+y^6=z^7$
Reasoning behind the cross products used to find area
Is there a simple way to prove Bertrand's postulate from the prime number theorem?
Show that the dual space of the vector space of all polynomials is isomorphic to the infinite-dimensional Euclidean vector space over the reals
subdifferential rule proof
Normalizer of a Sylow 2-subgroups of dihedral groups
How can this integral expression for the difference between two $\zeta(s)$s be explained?
In how many ways can five letters be posted in 4 boxes?
Show that $P_{n}(x)\rightrightarrows 0\qquad (x\in[0,1])$