Advertisement
Published in:
2016 | OriginalPaper | Chapter
Peano Arithmetic and -Classes
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
One of the earliest purposes of computability theory was the study of logical systems and theories. We consider theories in a computable language: one which is countable, and whose function, relation, and constant symbols and their arities are effectively given. We also assume that languages come equipped with an effective coding for formulas and sentences in the languages, i.e., a Gödel numbering, and identify sets of formulas with the corresponding set of Gödel numbers. We can then speak of the Turing degree of a theory in a computable language