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ULTRA-COMBINATORICS. Applications of ultrafilters in combinatorial number theory, and related topics

Hypernatural numbers, idempotent ultrafilters and a proof of Rado's theorem.

speaker: Mauro Di Nasso (Università di Pisa)

abstract: The hypernatural numbers of nonstandard analysis can be used as representatives of ultrafilters on N. We give a characterisation of idempotent ultrafilters in nonstandard terms, and use it to show that suitable linear combinations of any given idempotent yield a proof of Rado's theorem.

timetable:
Thu 24 Jan, 16:30 - 17:10, Aula Dini
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