Did large cardinals exist before 1963?

Question

I'm curious to know the history of the interaction between large cardinals and traveling to (creating) universes through forcing. The question arose because I understand that Peano Arithmatists force, but it is like a large cardinal embedding in that it forces the existance of an inner model. When was the first large cardinal introduced and was it viewed as a way to create a model of set theory? Were large cardinals considered before Cohen first forced?

Answer 1

Very much so.

Measurable cardinals were considered by Banach and Kuratowski in 1929 and 1930. In 1943 Tarski proved that measurable cardinals are weakly compact, although the definition by tree properties and by coloring were given only in 1961 by Erdos and Tarski.

Hausdorff worked with weakly inaccessible cardinals, and Mahlo defined what is now known as Mahlo cardinals, Sierpinski and Tarski defined strongly inaccessible cardinals, as well Zermelo worked with them (e.g. he proved that the only models of $\sf ZFC_2$ are $V_\kappa$ for strongly inaccessible $\kappa$). All these things were well before the 1950's.

All this is just from the brief historical remarks in Jech's Set Theory (Chapters 9 and 10), brief excerpts from the introduction of Kanamori's wonderful The Higher Infinite.

Scott's theorem, by the way, that a measurable cardinal implies $V\neq L$ was published in 1961.