Show that an infinite map can be colored with four colors iff each of its submaps can be colored with four colors. Hint: Take a language that has constant symbols for each country and that has four predicate symbols of an argument for colors. Use the compactness theorem.
Show that an infinite map can be colored with four colors iff each of its submaps can be colored with four colors. Hint: Take a language that has constant symbols for each country and that has four predicate symbols of an argument for colors. Use the compactness theorem.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 41E: Express (AB)(AB) in terms of unions and intersections that involve A,A,B,andB
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Mathematical Logic
Validity, completeness, and models in first-order logic
Show that an infinite map can be colored with four colors iff each of its submaps can be colored with four colors. Hint: Take a language that has constant symbols for each country and that has four predicate symbols of an argument for colors. Use the compactness theorem.
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