logical deduction - Infinite choice question

The assertions in the following infinite list are all the same, true or false.
      $~\vdots$
  T$~~$F $~~$ I have a black Model T.
  T$~~$F $~~$ I have a black Model T.
  T$~~$F $~~$ I have a black Model T.

      $~\vdots$

The object is to concoct an infinite list of assertions where: $\strut$
•   The assertions are identical. $\strut$
In every possible consistent scenario where each assertion is either true or false: $\strut$
•   At least one assertion must be true. $\strut$
•   At least one assertion must be false. $\strut$
And at least one consistent scenario is possible.

In this open-ended challenge infinitely many answers are possible.
Try to find one (or more) in any (or none) of these categories. $\strut$
a.  Exactly one assertion must be true.

b.  Exactly one assertion must be false.
c.  Infinitely many assertions must be true
   while infinitely many must be false.
d.  Some other quirky condition.
e.  Some other quirky condition.
f.   Some other quirky condition.
      $~\vdots$

Feeling competitive?$~$ Try for the fewest words.

Here's an answer that is incorrect because the truth values could be all true:

      $~\vdots$
  T$~~$F $~~$ This assertion is true.
  T$~~$F $~~$ This assertion is true.
      $~\vdots$

Here's an answer that is incorrect because the assertions can be neither true nor false:
      $~\vdots$
  T$~~$F $~~$ This assertion is false.
  T$~~$F $~~$ This assertion is false.
      $~\vdots$

Answer

Answers without a ** next to them work only if the list is countably infinite and ordered (although an ordering could be enforced in the assertion at the cost of brevity).

a**:

Other assertions are False

If this is true for any assertion, all other assertions are false. If this is false for any assertion, a true assertion must exist. The combination of these two facts guarantees exactly one true assertion.

b**:

Another assertion is False

If this is false for any assertion, then all other assertions are true. If this is true for any assertion, a false assertion must exist. The combination of these two facts guarantees exactly one false assertion.

c:

Next assertion is False

If the first assertion is true, the next is false, which makes the next true... etc. The inverse is also possible, but either way, infinite assertions are both true and false.

d**:

Other [property] assertions are False

This allows you to make any single assertion true. For example, if you want only assertion 18 to be true, pick the property [18th]. This is vacuously true for the 18th assertion, since no other 18th assertions exist. Since the 18th assertion is true, every other assertion is false.

Another [property] assertion is False

This allows you to make any single assertion false. For example, if you want only assertion 18 to be false, pick the property [18th]. This is false for the 18th assertion, since no other 18th assertions exist to have truth values. Since the 18th assertion is false, every other assertion is true.

[X] other [property] assertions are True

Through similar logic, this allows you to make any finite number of specific assertions true, with the rest false.

[X] other [property] assertion are False

Through similar logic, this allows you to make any finite number of specific assertions false, with the rest true.

And finally, the universal (if boring) e**:

[Property] assertion

This lets you cause any describable set of assertions to be true, with the rest false. It also implies some cheesy ways of doing a, b, and c.

a:

First assertion

Obviously, true only of the first assertion.

b:

Subsequent assertion

True of all but the first assertion.

c:

Prime assertion

True and false for infinitely many assertions.