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Ax–Schanuel for linear differential equations
Archive for Mathematical Logic 57 (5-6):629-648 (2018)
Abstract
We generalise the exponential Ax–Schanuel theorem to arbitrary linear differential equations with constant coefficients. Using the analysis of the exponential differential equation by Kirby :445–486, 2009) and Crampin we give a complete axiomatisation of the first order theories of linear differential equations and show that the generalised Ax–Schanuel inequalities are adequate for them.Other Versions
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Citations of this work
Adequate predimension inequalities in differential fields.Vahagn Aslanyan - 2022 - Annals of Pure and Applied Logic 173 (1):103030.
Index Locorum.Henri Atlan - 2024 - In Spinoza and Contemporary Biology: Lectures on the Philosophy of Biology and Cognitivism. Edinburgh: Edinburgh University Press. pp. 533-542.
References found in this work
Pseudo-exponentiation on algebraically closed fields of characteristic zero.Boris Zilber - 2005 - Annals of Pure and Applied Logic 132 (1):67-95.
On the decidability of the real exponential field.Angus Macintyre & Alex J. Wilkie - 1996 - In Piergiorgio Odifreddi, Kreiseliana: About and Around Georg Kreisel. A K Peters. pp. 441--467.
Model theory of special subvarieties and Schanuel-type conjectures.Boris Zilber - 2016 - Annals of Pure and Applied Logic 167 (10):1000-1028.
Definability of derivations in the reducts of differentially closed fields.Vahagn Aslanyan - 2017 - Journal of Symbolic Logic 82 (4):1252-1277.
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