A note on Kunen
Both of Kunen's textbooks use nonstandard notation. The most important deviations are:
- R(α) denotes the levels of the cumulative hierarchy of sets, normally denoted by Vα
- ON denotes the class of Ordinals
- HF denotes the set of "hereditarily finite sets", usually denoted by Vω
- ZC denotes ZFC − Replacement. Z denotes ZF − Replacement. ZFC − is ZFC − Foundation and ZF − is ZF − Foundation.
Kunen sometimes puts emphasis on proving results in ZFC without the Axiom of Foundation first (later showing that the cumulative hierarchy of sets V, which doesn't require Foundation to be defined, satisfies ZFC with Foundation). We will not be concerned with this so you can always assume that Foundation is a ZFC axiom and skip any discussion of Kunen that relates to Foundation. Whenever Kunen assumes ZFC − or ZF − , you can exchange it with ZFC or ZF, respectively.