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+title = "Different logical foundations"
+author = "Yann Herklotz"
+tags = []
+categories = []
+backlinks = ["4c"]
+forwardlinks = ["4c2"]
+zettelid = "4c1"
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+
+There are different logical foundations to mathematics. The main one
+that is used is Zermelo-Fraenkel set theory with the axiom of choice
+(ZFC). However, there can be alternatives. For example, type theory
+provides and alternative basis for the theory of mathematics, and also
+result in a different logic.
+
+Propositional logic always needs set theory as a base to work with,
+however, logical systems like intuitionistic logic can be built up using
+type theory without ever needing set theory.