
Add the following items to the bibliography:

Kolany, A.

[1999] Rad\`o selection lemma and other combinatorial statements uniformly
proved, preprint.

Herrlich, H./Keremedis, K.

[1998] Products, the Baire category theorem, and the axiom of dependent choice,
preprint October 12.

Add Goldblatt [1985] as a reference for form [345 A].

In form [43 D] add the word "filter": "... there is a ${\Cal D}$ generic
filter $G$ with $p\in G$."

Forms [14 CM] and [43 W] through [43 AC] have been added. Also, the first
definition in note 28 has been revised. For these additions and revisions
choose one of the two below:
Put [14 CM] in CHOICE FORMS, V. Conditional Choice and put [43 W] through
[43 AC] in TOPOLOGICAL FORMS I. Baire Category Type Theorems and in II. Product
Theorems.

In the bibliography, change Banaschewski [1998] to:

[1998] Choice functions and compactness conditions , Math. Logic Quart.
44, 427430.
change Felgner, U./Truss, J. K. [1999] to:

[1999] The independence of the prime ideal theorem from the order extension
theorem , Fund. Math. 64, 199215.
and change Keremedis, K./Tachtsis, E. [1999] to:

Howard, P./Keremedis, K./Rubin, J./Stanley, A./Tachtsis E.,

[1999] Nonconstructive properties of the real numbers , preprint.

Add the following items to the bibliography:

Keremedis, K./Tachtsis, E.

[1999a] On Loeb and weakly Loeb Hausdorf spaces preprint.

Keremedis, K./Tachtsis, E.

[1999b] The countable axiom of choice for finite sets does not imply compact
metric spaces are separable preprint.

Add the two forms:

[5 A] Partial Choice for Countable Families of Countable Sets of Reals: Every
countable family of nonempty countable sets of real numbers has an infinite
subset with a choice function. (See the proof of the equivalence of 94 and
[94 N].)

FORM 338. $UT(\aleph_0,\aleph_0,WO)$: The union of a denumerable number of
denumerable sets is well orderable. Note 4.

Add [5 A] to CHOICE FORMS, Part IV, Partial Choice and add form 338 to CARDINAL
NUMBER FORMS, Part III Cardinality of Unions.

Form [8 F] should be a new form, form 339. This leaves [8 F] blank.

FORM 339. Martin's Axiom $(\aleph_{0})$: Whenever $(P\le)$ is a nonempty,
ccc quasiorder (ccc means every antichain is countable) and ${\Cal D}$
is a family of $\le\aleph_0$ dense subsets of $P$, then there is a ${\Cal
D}$ generic filter $G$ in $P$. Kunen [1980], Shannon [1990], and note 47.

Remove [8 F] and add form 339 to ORDERING RELATIONS, Part II, Versions of
Martin's Axiom.

It was shown in Howard/Keremedis/Rubin/Stanley [1999] that forms 6 and 36
are equivalent. Thus, omit form 36 and add form [6 C]:
[6 C] If $A\subseteq{\Bbb R}^n$ and $A\bigcap B$ is countable for
every bounded $B$ then $A$ is countable. G. Moore [1982] p 36,
Keremedis/Howard/Rubin/Stanley/Tachtsis [1999].

Add a new form 36:
FORM 36. Compact T$_2$ spaces are Loeb. (A space is Loeb if
the set of nonempty closed sets has a choice function.) Keremedis/Tachtsis
[1999a].