## Reverse mathematics 2001Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting recent developments in reverse mathematics and subsystems of second order arithmetic. |

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ACAo algebra Archimedean assume ATRo axioms blocking pair BTFA claim co-model coded compact complete separable metric computable construction continuous embedding continuous function contradiction Corollary countable well orderings define definition denote exists following are equivalent following is provable free set graph H Lemma H Theorem Hence implies induction infinite path initial segment isomorphic least element limit point linear ordering metric space n-colorable natural numbers nonempty nonstandard Notes in Logic ordered group ordinal parameters Peano arithmetic poset primitive recursive promptly simple proof of Theorem provable in RCAo quasi-ordering r.e. degrees Ramsey's theorem RCAo real numbers requirements result reverse mathematics rk(x satisfies saturated models scheme second order arithmetic sentences separable metric space stable marriage problem stable matching subgroup subset subsystems of second Suppose Symbolic Logic tail well founded Theorem 2.2 theory upper bound WKLo