Archive for Mathematical Logic

, Volume 57, Issue 3–4, pp 429–451 | Cite as

Decidability of the AE-theory of the lattice of \({\varPi }_1^0\) classes

  • Linda Lawton


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.


Lattice Computability Decidability \({\varPi }^0_1\) class 

Mathematics Subject Classification

03D 03G10 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Northern Michigan UniversityMarquetteUSA

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