Roman Sikorski
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High Quality Content by WIKIPEDIA articles! This result confirmed that semialgebraic sets in Rn form what is now known as an o-minimal structure on R. These are collections of subsets Sn of Rn for each n 1 such that we can take finite unions and complements of the subsets in Sn and the result will still be in Sn, moreover the elements of S1 are simply finite unions of intervals and points. The final condition for such a collection to be an o-minimal structure is that the projection map on the first n coordinates from Rn+1 to Rn must send subsets in Sn+1 to subsets in Sn. The Tarski Seidenberg…mehr

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High Quality Content by WIKIPEDIA articles! This result confirmed that semialgebraic sets in Rn form what is now known as an o-minimal structure on R. These are collections of subsets Sn of Rn for each n 1 such that we can take finite unions and complements of the subsets in Sn and the result will still be in Sn, moreover the elements of S1 are simply finite unions of intervals and points. The final condition for such a collection to be an o-minimal structure is that the projection map on the first n coordinates from Rn+1 to Rn must send subsets in Sn+1 to subsets in Sn. The Tarski Seidenberg theorem tells us this holds if Sn is the set of semialgebraic sets in Rn.