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In this paper a new proof of the strong normalization theorem (SN) for barrecursive terms is presented.
In this note, we answer the following question: Given two recursively presented well orderingsR, S of subsets of the natural numbers, what is the complexity of an ordinal comparison mapκ takingR isomorphically onto an initial segment ofS (or vice versa)?
An extension of a Tauberian theorem of Hardy and Littlewood is proved. It is used to show that, for classes of finite models satisfying certain combinatorial and growth properties, Cesàro probabilities (limits of average probabilities over second order sentences) exist. Examples of such classes...
In this paper we exposit some as yet unpublished results of Harvey Friedman. These results provide the most dramatic examples so far known of mathematically meaningful theorems of finite combinatorics which are unprovable in certain logical systems. The relevant logical systems,ATR
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