Full Idea
Skolem and Gödel were the main proponents of first-order languages. The higher-order language 'opposition' was championed by Zermelo, Hilbert, and Bernays.
Gist of Idea
Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 7.2)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.178