Reports on Mathematical Logic

No. 37


On the First Order Logic true in every universe (including the empty universe)

A b s t r a c t. As it is well known, the set of theorems: $Th_{LP}$ of the first order predicate calculus $LP$ contains all formulae which are valid in every universe with non-empty set of individuals. In this paper I investigate a certain restriction $LM$ of $LP$. Its set of theorems contains only the theorems valid also in the ''empty-universe'' (i.e.\ in the universe with empty set of individuals).

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