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Would a proposition of first-order logic, with N quantifiers, always held the same logical status (of consistency or validity) no matter if the domain has N members, or N + x members? [x being a finite number]

I intuitively think the answer is YES, but what about any kind of proof?!

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    I corrected "n finite" to "a finite". If you meant "an infinite" please fix it.2012-03-21
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    It sounds like you might have an odd conception of quantifiers. Could you say what you think quantifiers are, how they work, or what your own reasoning about the answer is?2012-03-23

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