4. In a BB universe that is homogeneous, isotropic, and devoid of preferred reference frames, this logical iteration can be carried out forever, projecting to an infinite number of "visible universes" each centered on a unique observer. Therefore, if the BB universe is flat or open (and most adherents of standard cosmology are solidly wedded to flat at a minimum, and perhaps open), it must also be spacially infinite.
This is a logical proof derived from the principles of the standard model. I would attempt to simplify it further, but refrain for fear of loss of coherence.
How could the BB universe possibly be finite? To model a
finite BB universe, either at least one the three assumptions made by the standard model about the basic qualities of the universe must be wrong, OR the universe must assume a complex topology that somehow both keeps the universe flat/Euclidean locally AND bends space in such a way that one can set off in one direction and come back upon one's previous location without deviating from a straight path. Such theoretical topologies are apparently not falsifiable by any means, and absent any compelling reason to embrace them (apart from sheer revulsion at the thought of infinities

) there is presently no need to regard them as anything more than mathematical curiosities.
I welcome any logical refutation of this proof. "Carpet-bombing" this post with citations that do not address the logic of the proof and simple nay-saying will be cheerfully ignored.

Is there a logical failure in this proof? I would love to see it.