… of N18 in [5] (which relies on an ultrafilter on ω). Using the fact that C(WO, WO… on a modification
of the proof in [5], we will present a complete proof of the independence result, based on …

… models of set theories for which certain axioms are given. In § 1 I first mention some general
forms of the comprehension axiom and then prove a further theorem on the model in [1]. In § …

… union of the family 9: S = u{X: Xe 9). Using a well-ordering < of S, we define a choice function
f on … character of the axiom makes it less self evident than other axioms, we have to ask …

… The author is grateful to the many people who have commented on drafts of this paper.
AXIOM's philosophy AXIOM shares with … The operations available on this union domain are: …

… union axiom of ZFC. After a brief introduction, we sketch a proof of the folklore result that union
is independent of the other axioms … The purpose of this paper is to study the union axiom …

… Among those whose work on the subject has had most influence on this book are (apart …
The functions tp, PEI, are pairwise compatible and thus their union is a binary function f on S …

… on true axioms, and that our rules of inference preserve truth. The next question, naturally, is
why we believe the axioms, … of Choice, including the fact that a countable union of countable …

… that no contradictions can be derived from the axioms of ZFC. … such a result can be reformulated
as a result on consistency. … the following axiom system is consistent: ZFC +'the union of ~…

… I will typically use P, Q, R, I, J, K and INIT to denote total predicates on … on how they were
proved. (Compare with the vague discussion of the union theorem and the substitution axiom in …

… Let C be the base on S1 such that f : ([0, 1], … on [0, 1] generated by B (note that T1 is the
topology on [0, 1] induced by the usual topology of the real line), and letting T2 be the topology on …