  Frege's and Peano-Russell's approach to logic became the universally  accepted one, especially through the influence of Hilbert and his  co-workers in the 1920s. In the 19th century, Frege was a marginal  figure, and the algebraic approach to logic, as in Boole and  especially Ernst Schröder, was the dominant one. It is clear  that there was a good understanding of the principles of predicate  logic in this tradition, for how could there have been a  Löwenheim-Skolem theorem otherwise? Skolem found out about  Frege's logic through Principia Mathematica only after having  worked out the theorem in his paper of 1920. The first section of  that paper, widely read because of the English translation in Van  Heijenoort's From Frege to Gödel, marks the end of the  algebraic tradition of logic that merged silently with lattice  theory. Other sections of the paper contain a remarkable beginning of the analysis of proofs in lattice theory and in projective geometry:  Skolem considered the axioms of a mathematical theory from a purely  combinatorial and formal point of view, as means for producing  derivations of a formula from given formulas used as assumptions. It  was found out in the early 1990s that the part on lattice theory  contains the solution of a decision problem, called the word problem  for freely generated lattices, the known solution of which stemmed  from 1988! Skolem's terminology and notation in lattice theory are  those of Schröder and that is part of the reason why his work  was a lost opportunity for proof theory.