 Brouwer, Luitzen Egbertus Jan |  category theory |  choice, axiom of |  Gödel, Kurt |  -->Hilbert, David--> |  Hilbert, David: program in the foundations of mathematics |  logic, history of: intuitionistic logic |  logic: classical |  logic: intuitionistic |  mathematics, philosophy of: formalism |  mathematics: constructive |  phenomenology |  Platonism: in metaphysics |  set theory |  type theory 