Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
A First-Order Definition For Campana Points In $\Mathbb Q$
In 2010 J.\ Koenigsmann showed that $\mathbb Z$ is a first-order universally defined subset of $\mathbb Q$; or, equivalently, that the set of non-integer rationals is a diophantine subset of $\mathbb Q$. Using the same techniques, K.\ Eisentraeger and T.\ Morrison generalized that result to $S$-integers. Here we give a simpler proof of this, and we obtain a less complex formula which is uniform over all finite sets of primes. We apply our techniques to give an $\forall\exists$ first order definition for Campana points in $\mathbb Q$.
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A First-Order Definition For Campana Points In $\Mathbb Q$
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