In this paper we shall be concerned with questions regarding decision problems for certain classes of sentences (without quantifiers) of various kinds of algebra. In the first section we shall establish a result of a general nature, which enables one, in a number of cases, to reduce a decision problem of the type considered to a somewhat simpler problem. In the second section we formulate a rather broad sufficient condition for the existence of a decision method for sentences without quantifiers; and in the last section we show that this condition holds of lattices.
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J. C. C. McKinsey (1943) studied this question.