Even though real arithmetic is uncountable, it possesses a countable "model."
Skolem Paradox
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References
Curry, H. B. Foundations of Mathematical Logic. New York: Dover, pp. 6-7, 1977.Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 191-192, 1998.Referenced on Wolfram|Alpha
Skolem ParadoxCite this as:
Weisstein, Eric W. "Skolem Paradox." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SkolemParadox.html