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This graduate-level book is well known for its proof that many
mathematical systems--including lattice theory, abstract projective
geometry, and closure algebras--are undecidable. Based on research
conducted from 1938 to 1952, it consists of three treatises by a
prolific author who ranks among the greatest logicians of all time.
The first article, "A General Method in Proofs of Undecidability,"
examines theories with standard formalization, undecidable
theories, interpretability, and relativization of quantifiers. The
second feature, "Undecidability and Essential Undecidability in
Mathematics," explores definability in arbitrary theories and the
formalized arithmetic of natural numbers. It also considers
recursiveness, definability, and undecidability in subtheories of
arithmetic as well as the extension of results to other
arithmetical theories. The compilation concludes with
"Undecidability of the Elementary Theory of Groups."
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