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arXiv · 2512.05772

Skolemization and Decidability of the Bernays-Schoenfinkel Class in Goedel Logics

Mariami Gamsakhurdia·Matthias Baaz·Anela Lolic
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Abstract

In 1928, Bernays and Schoenfinkel proved the decidability of prenex sentences whose matrices contain no function symbols, now known as the Bernays-Schoenfinkel (BS) class. We investigate the decidability of the BS class for all Goedel logics. Our validity argument relies on the fact that Skolemization works for prenex Goedel logics, while 1-satisfiability follows from structural properties of prenex formulas. We show that validity and 1-satisfiability for the BS class are decidable in every Goedel logic, and that these properties persist across all infinite Goedel logics.

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Mariami Gamsakhurdia, Matthias Baaz, Anela Lolic. 2025-12-05. Skolemization and Decidability of the Bernays-Schoenfinkel Class in Goedel Logics. https://arxiv.org/abs/2512.05772

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