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Logic seminar

Elementary analytic functions in VTC^0

Emil Jeřábek


Monday, 17. October 2022 - 16:00 to 17:30
Large lecture room at Zitna and online at - contact before the meeting to join online
It is known that rational approximations of elementary analytic functions (exp, log, trigonometric and hyperbolic functions, and their inverse functions) are computable in the complexity class TC^0. In this talk, we will show how to formalize their construction and basic properties in the correspoding arithmetical theory VTC^0, working with completions of fraction fields of models of VTC^0. As a consequence, we will show that every countable model of VTC^0 is an exponential integer part of a real-closed exponential field, using a recursive saturation argument.