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pooj4
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There are an infinite number of natural numbers. Why is that? Well this follows from the following facts:
(i) There is at least one natural number.
(ii) For each natural number there is a distinct number which is its successor, i.e., for each number $x$ there is a distinct number $y$ such that $y$ stands in the
successor relation to $x$.
(iii) No two natural numbers have the same successor.
(iv) There is a natural number, namely 0, that is not the successor of any number.Bearing these facts in mind, what's a formula in first-order logic that that is satisfiable by a valuation only if the domain of the valuation is infinite. Contain some non-logical vocabulary in presentation of course.
(i) There is at least one natural number.
(ii) For each natural number there is a distinct number which is its successor, i.e., for each number $x$ there is a distinct number $y$ such that $y$ stands in the
successor relation to $x$.
(iii) No two natural numbers have the same successor.
(iv) There is a natural number, namely 0, that is not the successor of any number.Bearing these facts in mind, what's a formula in first-order logic that that is satisfiable by a valuation only if the domain of the valuation is infinite. Contain some non-logical vocabulary in presentation of course.
