Séminaires : Séminaire de Logique Lyon-Paris

Equipe(s) : lm,
Responsables :S. Anscombe, O. Finkel, A. Khélif, S. Rideau, T. Tsankov, A. Vignati
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Salle : ID de réunion : 825 2397 5662 Code secret : 523743
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Orateur(s) Mickaël Matusinski - Université de Bordeau,
Titre Surreal numbers with exponential and omega-exponentiation
Horaire16:00 à 17:15
Diffusion https://u-paris.zoom.us/j/82523975662?pwd=dXh5M095TC92dUlwek50d0ZoWFdNdz09
RésumeIntroduced by Conway to evaluate partial combinatorial games, surreal numbers consist in a proper class containing "all numbers great and small". Moreover, they can be endowed with a very rich algebraic and even analytic structure, turning them into universal domains for several important theories : linearly ordered sets, ordered Abelian groups, ordered valued fields - in particular ordered generalized series fields via the omega-exponentiation -, real analytic fields and exponential fields, and more recently H-fields (an abstract version of Hardy fields due to M. Aschenbrenner and L. van den Dries). In this talk, I will introduce these fascinating objects, starting with the very basic definitions, and will give a quick overview, with a particular emphasis on exp (which extends exp on the real numbers) and the omega map (which extends the omega-exponentiation for ordinals). This will help me to subsequently present our recent contributions with A. Berarducci, S. Kuhlmann and V. Mantova concerning the notion of omega-fields (possibly with exp). One of our motivations is to clarify the link between composition and derivation for surreal numbers.
SalleID de réunion : 825 2397 5662 Code secret : 523743