Decidability of the AE-theory of the lattice of $${varPi }_1^0$$ classes |
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| Authors: | Linda Lawton |
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| Affiliation: | 1.Northern Michigan University,Marquette,USA |
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| 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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