Decidability and definability in first-order theories of real addition with order

Target entity: Decidability and definability in first-order theories of real addition with order
Context triple: [Robert Shostak, doctoralThesis, Decidability and definability in first-order theories of real addition with order]

• A. On definable sets of real numbers
  "On definable sets of real numbers" is a seminal essay in mathematical logic and set theory that investigates which subsets of the real line can be precisely characterized or defined within formal systems.
• B. Tarski’s theorem on the completeness of elementary algebra and geometry
  Tarski’s theorem on the completeness of elementary algebra and geometry is a foundational result in mathematical logic showing that the first-order theory of real closed fields (capturing elementary algebra and Euclidean geometry) is complete, decidable, and admits quantifier elimination.
• C. Tarski–Seidenberg theorem
  The Tarski–Seidenberg theorem is a fundamental result in real algebraic geometry stating that projections of semialgebraic sets are again semialgebraic, underpinning quantifier elimination over the real numbers.
• D. “A Decision Method for Elementary Algebra and Geometry”
  “A Decision Method for Elementary Algebra and Geometry” is Alfred Tarski’s influential work that presents a procedure for deciding the truth of statements in elementary algebra and geometry, laying foundations for decision theory in mathematical logic.
• E. Hilbert’s tenth problem
  Hilbert’s tenth problem is a famous unsolved question in mathematics that asked for a general algorithm to determine whether any given Diophantine equation has an integer solution, and whose negative answer helped establish fundamental limits of computability.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Decidability and definability in first-order theories of real addition with order
Target entity description: "Decidability and definability in first-order theories of real addition with order" is Robert Shostak’s doctoral thesis in mathematical logic, focusing on the logical properties and algorithmic solvability of theories involving ordered real addition.

• A. On definable sets of real numbers
  "On definable sets of real numbers" is a seminal essay in mathematical logic and set theory that investigates which subsets of the real line can be precisely characterized or defined within formal systems.
• B. Tarski’s theorem on the completeness of elementary algebra and geometry
  Tarski’s theorem on the completeness of elementary algebra and geometry is a foundational result in mathematical logic showing that the first-order theory of real closed fields (capturing elementary algebra and Euclidean geometry) is complete, decidable, and admits quantifier elimination.
• C. Tarski–Seidenberg theorem
  The Tarski–Seidenberg theorem is a fundamental result in real algebraic geometry stating that projections of semialgebraic sets are again semialgebraic, underpinning quantifier elimination over the real numbers.
• D. “A Decision Method for Elementary Algebra and Geometry”
  “A Decision Method for Elementary Algebra and Geometry” is Alfred Tarski’s influential work that presents a procedure for deciding the truth of statements in elementary algebra and geometry, laying foundations for decision theory in mathematical logic.
• E. Hilbert’s tenth problem
  Hilbert’s tenth problem is a famous unsolved question in mathematics that asked for a general algorithm to determine whether any given Diophantine equation has an integer solution, and whose negative answer helped establish fundamental limits of computability.
• F. None of above. chosen