 The next crucial steps into the “very high” infinite were done in 1930. The notion of strongly inaccessible cardinals was then isolated by Sierpiński &amp; Tarski, and by Zermelo [1930]. A strong inaccessible is a regular cardinal \(\alpha\) such that \(2^x\) is less than \(\alpha\) whenever \(x &lt; \alpha\). While weak inaccessibles merely involve closure under the successor operation, strong inaccessibles involve a much stronger notion of closure under the powerset operation. That same year, in a path-breaking paper on models of ZFC, Zermelo [1930] established a link between the uncountable (strongly) inaccessible cardinals and certain “natural” models of ZFC (in which work he assumed that the powerset operation is, so to say, fully determinate).