Abstract
An AE-sentence is a sentence in prenex normal form with all universal quantifiers preceding all existential quantifiers, and the AE-theory of a structure is the set of all AE-sentences true in the structure. We show that the AE-theory of \((\mathscr {L}({\varPi }_1^0), \cap , \cup , 0, 1)\) is decidable by giving a procedure which, for any AE-sentence in the language, determines the truth or falsity of the sentence in our structure.
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Lawton, L. Decidability of the AE-theory of the lattice of \({\varPi }_1^0\) classes. Arch. Math. Logic 57, 429–451 (2018). https://doi.org/10.1007/s00153-017-0564-5
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DOI: https://doi.org/10.1007/s00153-017-0564-5