This video introduces (first-order) structures. The two running examples in the session are graphs and groups. Then the video presents three general definitions for structures: substructures+extensions, reducts+expansions, and homomorphisms. The Hadwiger-Nelson problem is mentioned as an open problem about homomorphisms where the compactness theorem for first-order logic is useful. Another application of the compactness theorem for first-order logic is Levi's theorem for Abelian groups. The video contains two breaks.
