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Undecidable Theories
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."
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."
Reprint of the North-Holland Publications, Inc., Amsterdam, 1953 edition.
foundational mathematics;logic;theory;math and science;mathematics;arithmetic;subtheories of arithmetic;advanced study of mathematics;mathematical systems;lattice theory;abstract projective geometry;closure algebras;20th century research;technical writing;mathematical data;math;scientific research;applied mathematics;graduate level math;model theory;meta mathematics;essential undecidabilty;group theory;pure mathematics; Undecidable theories; Alfred Tarski; Undecidability; Foundations of mathematics; Godel's Theorum$5.93
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Description
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."
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."
Reprint of the North-Holland Publications, Inc., Amsterdam, 1953 edition.
foundational mathematics;logic;theory;math and science;mathematics;arithmetic;subtheories of arithmetic;advanced study of mathematics;mathematical systems;lattice theory;abstract projective geometry;closure algebras;20th century research;technical writing;mathematical data;math;scientific research;applied mathematics;graduate level math;model theory;meta mathematics;essential undecidabilty;group theory;pure mathematics; Undecidable theories; Alfred Tarski; Undecidability; Foundations of mathematics; Godel's Theorum
