Definition of "ZF"

Gödel's model is an example of a simple type of inner model that might be called a definable transitive inner model3), where the universe is replaced by a transitive subuniverse defined within ZF, the membership relation is just the original one restricted to the subuniverse, and where the axioms of ZF relativized to the subuniverse, are provable within ZF.

1967, Carol Karp, “A Proof of the Relative Consistency of the Continuum Hypothesis”, in John N. Crossley, editor, Sets, Models, and Recursion Theory, North-Holland, page 7

1. Corollary: ZF is not finitely axiomatizable. / 2. Corollary: ZF is reflexive (i.e. the consistency of every finite subtheory of ZF can be proved within ZF).

1971, Ulrich Felgner, Models of ZF-Set Theory, Springer, Lecture Notes in Mathematics 223, page 21

However, the problem with it,[the generalized continuum hypothesis] and the reason why it is not part of ZF strictly (apart from the fact that it implies the axiom of choice) is that it is rather arbitrary.

1991 [Kluwer Academic], Fred Landman, Structures for Semantics, 1991, Springer, Softcover, page 56

In the case of the ZF detector, we suppress the interference among the transmit streams by multiplying the received signal vector y with the Moore-Penrose pseudo-inverse of the channel matrix […]

2008, Byeong Gi Lee, Sunghyun Choi, Broadband Wireless Access and Local Networks

However, due to its simplicity, ZF equalization is a good choice when the channel is known and fixed, and also when there is no frequency notch in the channel frequency response […]

2010, Dayan Adionel Guimaraes, Digital Transmission, page 348

Thus, the importance of the upper bound is in showing that even in the most optimistic case, the achievable rate cannot exceed the ZF rates by more than 10%.

2013, Academic Press Library in Signal Processing, page 308