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Bare canonicity of representable cylindric and polyadic algebras

<11>Paper proves fundamental exotic limitative theorem on nature of axiomatisations of finite-dimensional representable cylindric and polyadic algebras, with implications for axiomatisations of finite-variable first-order logics. Line of work began with Hodkinson-Venema (2003), continued in modal logic by Goldblatt-Hodkinson (2007), and Kikot who incorporated it into a dichotomy for modal logics. Proof technique simplified and generalised here - uses algebras from submission 2, games, duality, compactness, Ramsey theory, random graphs. Published version of final-year undergraduate project (designated Distinguished, awarded Donald Davies prize) by Bulian, now PhD student of Dawar at Cambridge.