Decision Procedures for Elementary Sublanguages of Set Theory: X. Multilevel Syllogistic Extended by the Singleton and Powerset Operators

Excerpt from Decision Procedures for Elementary Sublanguages of Set Theory: X. Multilevel Syllogistic Extended by the Singleton and Powerset Operators

The intended meaning of the language is that in which variables range over (possibly infinite) sets in the standard universe of 'naive' set theory, and the var ious standard set-theoretic Operator and predicate symbols have their standard meanings; hence an interpretation M of a set of sentences d) of our language is a function which maps every variable a: into a set M 2. If all the sentences of p are true under some interpretation of this kind, is said to be satisfiable and each interpretation which satisfies P is called a model of (note that all our considerations are easily formalizable in zpo, and in fact even in weaker set-theoretical systems, since the language with which we work includes only a very few constructs. But we will not belabor this technical point since this paper is concerned with computational rather than foundational questions.)

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