2001 Changes and additions for the Consequences of the Axiom of Choice
Project

Changes in January, 2001

Add to the bibilography:

Ern\'e, M.

[2001] Constructive order theory, preprint.

For additions to the numerical list of forms click on one of the following:

For additions to the notes click on one of the following:

Changes in February

Add the form
[91 B] The Axiom of Choice for Pure Sets. If $X$ is a set of nonempty sets
and there are no atoms in the transitive closure of $X$, then $X$ has a choice
function. Note 75.
Put [91 B] in CHOICE FORMS, I. Choosing Single Elements.

In note 18 In the list of forms that are true in every FM model replace
(Each one of these 51 forms is implied by one of the following 13 forms:
6, 37, 91, 92, 130, 273, 305, 309, 313, 361, 363, 368, 369.)
with
(Each one of these 50 forms is implied by form 91.)

Add a paragraph to note 75:
We also note that PW (form 91) is equivalent to the axiom of choice for pure
sets ([91 B]). To see this note first that [91 B] implies that the power
set of an ordinal can be well ordered. Since every well ordered set is equivalent
to an ordinal we obtain [91 B] implies 91. For the other implication we use
the result from H. Rubin /J. Rubin [1985], theorem 5.7, that 91 implies AC
in ZF.

Changes in August (We would like to thank Horst Herrlich for correcting this
error.)

In form [34 E], change ``Lindelof" to ``weakly Lindelof" and add ``note 43''
to the reference.

In the last paragraph of note 107 change ``Lindelof" to ``weakly Lindelof".

Additions to the Bibiography:

Herrlich, H., Products of Lindelof T2spaces are Lindelof in some models
of ZF, preprint [2001].

Additions to the Numerical List of Forms:

[94 T] There exists a noncompact Lindelof T1space.

[94 U] There exists a noncompact Lindelof subspace of R.

[94 V] There exists an unbounded Lindelof subspace of R.

[94 W] There exists a nonclosed Lindelof subspace of R.