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"... elementarily generated modal logics Abstract. In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form ∀x0∃x1...∃xn∧xiRλxj. We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a s ..."

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elementarily generated modal logics Abstract. In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form ∀x0∃x1...∃xn∧xiRλxj. We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a set of canonical formulas or by a single generalised Sahlqvist formula, together with modal definability of the initial formula, either simultaneously hold or simultaneously do not hold.