## The Bernays-Schönfinkel-Ramsey class for set theory: semidecidability.(English)Zbl 1201.03007

The authors consider formulas in a first-order language for sets whose only non-logical symbols are the binary predicate symbols $$=$$ and $$\in$$, representing equality and membership, respectively, and which are in prenex normal form with the quantificational prefix of the form $$\exists^*\forall^*$$.
The question at hand is whether or not such a formula is satisfiable in the standard cumulative set hierarchy $$V=\bigcup_\alpha {\mathcal P}(V_\alpha)$$. The authors provide a semi-decision algorithm for this satisfiability problem.

### MSC:

 03B25 Decidability of theories and sets of sentences 03E99 Set theory
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### References:

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