I thought I’d attempt to come up with a consistent convention of classifying mathematical statements. To do so we will simply think of the collection of statements as a partially ordered set where is interpreted as . And for each statement/node/point there will be two -valued functions that represent the number of incoming and outgoing edges (i.e. immediate antecedents and consequences). A point will be called a corollary if it has one incoming edge. A point will be called a theorem if its set of successors is a “large” subset of the poset (even if it is a corollary). A point will be called a lemma if at least one of its immediate successors is a theorem. A point will be called an axiom if it has zero incoming edges. And a point will be called a proposition if it is none of the above.
affordable care act Atlanta Public School System authoritarianism C*-algebras calculus capitalism communism conservatism coxeter complexes coxeter groups curriculum democracy diagonalization differentiation distribution of resources distributions economics education filtration foundations functional analysis god grading grading policy graphs graph theory Haar measure Hilbert space homework homework policy income distribution knowledge language law liberalism libertarianism lie algebras logic math math education mathematics math terminology metamathematics MLA New Math obamacare operator algebras political policy projections punctuation relations (math) representations republic resources school cheating school funding science Sobolev spaces social inequality socialism Suslin trees taxes tax policy tax system teaching tensor products topological groups trees (math) universe utilitarianism utility von Neumann algebras weak derivatives wealth gap ZFC