= Continuum many one-types of the integer ring
{title2=$|S_1(\operatorname{Th}(\mathbb Z,+,\cdot,0,1))|=2^{\aleph_0}$}
For every <subset> of the standard <prime numbers>, prescribe exactly which of those primes divide a nonzero element. Every finite prescription is realized by the product of its finitely many positive <divisibility> requirements. <Compactness theorem> extends each prescription to a <complete one-type> of the <complete theory> of the <integer> <ring>. Different <subsets> give incompatible <partial types>. The <countable> <first-order language> supplies the matching upper bound.
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