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Let n be the structure (R; +,.). (The language is assumed to have equality and the parameters V, +, -_. N is the structure whose universe is the set R of real numbers and is such that + and.R are the usual addition and product operations.) a) Give a formula that defines in the interval [0, ∞). the set {2}. b) Give a formula that defines in c) Show that any finite union of intervals whose endpoints are algebraic is definable on n.

Let n be the structure (R; +,.). (The language is assumed to have equality and the parameters V, +, -_. N is the structure whose universe is the set R of real numbers and is such that + and.R are the usual addition and product operations.) a) Give a formula that defines in the interval [0, ∞). the set {2}. b) Give a formula that defines in c) Show that any finite union of intervals whose endpoints are algebraic is definable on n.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Mathematical Logic First-order or predicate logic. Please be as clear as possible. Explain your answer. Thank you. R are Let I be the structure (R; +,.). (The language is assumed to have equality and the parameters V, +, . . N is the structure whose universe is the set R of real numbers and is such that +® and the usual addition and product operations.) a) Give a formula that defines in the interval [0, ∞). the set {2}. b) Give a formula that defines in c) Show that any finite union of intervals whose endpoints are algebraic is definable on n. (The converse is also true; these are the only definable sets in the structure. But we will not prove this fact.) Please be as clear as possible. Explain your answer. Thank you very much.
Transcribed Image Text:Mathematical Logic First-order or predicate logic. Please be as clear as possible. Explain your answer. Thank you. R are Let I be the structure (R; +,.). (The language is assumed to have equality and the parameters V, +, . . N is the structure whose universe is the set R of real numbers and is such that +® and the usual addition and product operations.) a) Give a formula that defines in the interval [0, ∞). the set {2}. b) Give a formula that defines in c) Show that any finite union of intervals whose endpoints are algebraic is definable on n. (The converse is also true; these are the only definable sets in the structure. But we will not prove this fact.) Please be as clear as possible. Explain your answer. Thank you very much.
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