Axiom Of Choice

We have the following indirect implication of form equivalence classes:

149

$\Rightarrow$ 118 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
149 $\Rightarrow$ 67	The axiom of choice in topology, Brunner, N. 1983d, Notre Dame J. Formal Logic note-26
67 $\Rightarrow$ 89	On cardinals and their successors, Jech, T. 1966a, Bull. Acad. Polon. Sci. S'er. Sci. Math. Astronom. Phys.
89 $\Rightarrow$ 90	The Axiom of Choice, Jech, 1973b, page 133
90 $\Rightarrow$ 118	Horrors of topology without AC: A non-normal orderable space, van Douwen, E.K. 1985, Proc. Amer. Math. Soc.

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number	Statement
149:	$A(F)$ : Every $T_2$ topological space is a continuous, finite to one image of an $A1$ space.
67:	$MC(\infty,\infty)$ $(MC)$ , The Axiom of Multiple Choice: For every set $M$ of non-empty sets there is a function $f$ such that $(\forall x\in M)(\emptyset\neq f(x)\subseteq x$ and $f(x)$ is finite).
89:	Antichain Principle: Every partially ordered set has a maximal antichain. Jech [1973b], p 133.
90:	$LW$ : Every linearly ordered set can be well ordered. Jech [1973b], p 133.
118:	Every linearly orderable topological space is normal. Birkhoff [1967], p 241.

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