Are there simple textbooks on Morse-Kelley set theory for mathematicians who are not specialists in this field (like me)?
I know only J.L.Kelley's "General topology", but it does not contain many important things, in particular, the notion of rank of a set, and everything connected to it. Can anybody suggest me some reading on this topic?
See:
For more references, see Morse-Kelley set theory .
You can see also:
[page vii] the axiomatic approach used is that of Kelley and Morse, expounded in the appendix of Kelley (1955). It seems to the author that the Kelley, Morse system, or the closely related system of Godel (1940), is used more often than any others by working mathematicians when any question of the foundation of set theory arises. It has the advantage of minimizing the necessary discussion of the symbolism of set theory.
[page 112] Turning to another topic, we will now discuss the important notion of the rank of sets. Roughly speaking, we want to assign an ordinal $\rho x$ to each set $x$ in such a way that the magnitude of $\rho x$ measures the complexity of $x$.
Definition 15.16 $\rho$ is the unique function with domain $V$ such that for any set $x$,
$$\rho x = \bigcap \{ \alpha : \rho y < \alpha \text { for each } y \in x \}.$$
We call $\rho x$ the rank of the set $x$.
Thus $\rho x$ is the least ordinal $> \rho y$ for each $y \in x$.
