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definability by formulas in first-order logic, e.g. as explained at https://en.wikipedia.org/wiki/Definable_set, or as in J. Robinson's first-order definition of the integers in the field of rationals

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Are the definable hyper-reals, using quantifiers only over the standard reals and natural nu...

$\newcommand{\st}{\textrm{st}}\newcommand{\bR}{{\bf R}}\newcommand{\bN}{{\bf N}}$ I think the limit of any definable convergent sequence $(a_n)$ (including $e$) is definable by the formula $$\varphi(x …
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