Model Theory
Object 'Model Theory' belongs to the 'Branches Of Math' theme.Connection to Computability Theory:
Model theorists are sometimes interested in the computational complexity of the set of statements needed to axiomatize a given theory.
Connection to Graph Theory:One interesting and elementary connection between model theory and graph theory is the proof of the four color mapping theorem in the case of infinite graphs. Assuming the theorem in the finite case, the infinite case is a simple matter of applying the compactness theorem of model theory.
Connection to Abstract Algebra:Model theory provides generalizations, as well as alternate proofs, for certain advanced theorems from algebra.
Connection to Set Theory:Set theory is very closely related to model theory. The only reason the former isn't completely a subfield of the latter is the inconvenient fact that the class of all sets is a proper class, whereas model theorists want their models to have universes which are not proper models.
Connection to Linear Algebra:Some of the notions in linear algebra (such as the span of a set of vectors), which the undergraduate already finds quite general and abstract, are actually generalized much further in model theory.
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