Let Σ be an effectively countable set of formulas. Suppose that for each formula τ, either Σ⊨τ or Σ⊨¬τ. Prove that the set of tautological consequences of Σ is decidable.
Let Σ be an effectively countable set of formulas. Suppose that for each formula τ, either Σ⊨τ or Σ⊨¬τ. Prove that the set of tautological consequences of Σ is decidable.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section: Chapter Questions
Problem 3SGR
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Mathematical logic
Formula set properties.
Let Σ be an effectively countable set of formulas. Suppose that for each formula τ, either Σ⊨τ or Σ⊨¬τ. Prove that the set of tautological consequences of Σ is decidable.
Please be as clear as possible. Use definitions if necessary. Show and explain all the steps of the proof. Thank you.
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