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Keywords Algebraic basis, Hamel basis, algebraic dual, dual operator, linear partial differential operator, linear partial differential equation, solvability, existence of a solution, generalized solution, Schwartz distribution Borel-Cantelli lemma Erdős–Rényi Theorem Fourier transform Gaussian measures Kochen-Stone theorem Locally compact abelian group, Pontryagin–van Kampen duality, Fourier transform, nonstandard analysis, hyperfinite, infinitesimal, approximation MV-algebras Pontryagin-van Kampen duality Quantitative analysis R-trees, model theory, metric structures, continuous logic, real-valued structures, model completion, categoricity, stability Representation of integers, Internal set theory, Polynomial congruence Solovay reducibility, Lipschitz continuity, Hölder continuity, computable analysis Ultrafilters, Ultrapowers, Almost disjoint families, Banach spaces, epsilon-separated sets, Measurable cardinals factoring of integers, nonstandard analysis, unlimited integers, Dickson’s conjecture hyperfinite infinitesimal approximation local algebras locally compact abelian group metastability nonstandard analysis