http://dswarmsikhttkg7jgsoyfiqpj3ighupfrvuz5ri3lu5q2dlqyrpgk7ad.onion/notes/frege-ancestral.html
A preliminary definition required for his definition of the ancestral of \(R\) is \(F\) is hereditary in the R -series if and only if every pair of R -related objects \(x\) and \(y\) are such that \(y\) falls under \(F\) whenever \(x\) falls under \(F\). Formally ( KS §24), \[
\text{Her}_{xyz}(F_x,R_{yz})\equiv\forall x\forall y(Rxy \land Fx \to Fy))
\] Then, Frege’s definition of the strong \(R^*\) (Frege 1967, §26; Frege, 1980, §79): \[
R^*(a,b) \equiv \forall...