## Formal development of ordinal number theory and applications to consistency proofs |

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a=p+l aeNO asserts Assume the hypothesis assumption atomic statement atrt AV(s axiom scheme axioms of group Cla(x class of ordinals class statement class theorem class-statement collection of ordinals contains no free contradicts converse domain Cor.l Cornell University corres definition development of ordinal duction equivalence classes expressions Firestone free occurrences free variable statement Funct(t function F fvm(m Godel number holds iota operator lence model not containing n-tuple notation occur free omit Ordinal Number Theory ordinals are closed orem Orn(a Orn(b Orn(Ind(x Orn(p predicate of ML primed theorems Proof replacing all free s)Sat(m satisfy the hypothesis Scarsdale seg(x,s sequence seSq sets of ordinals smor seg(y,t smorr statement calculus statement of NF statement with respect strong induction Sub-case sufficient to prove Suppose theorem follows tions Word(s xeAV(s