Constructive transfinite number classes

Constructive Versions of Ordinal Number Classes

0. Introduction and summary. Almost from its beginning, the theory of ordinal numbers has included results which can, in a rather concrete sense, be viewed as theorems about notations for ordinal numbers. For example the theorems on polynomial normal forms for those ordinals that lie below the least e number can be understood as providing a certain unique notation of finite length for each such...

Transfinite Ordinals in Recursive Number Theory

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Constructive Type Classes in Isabelle

We reconsider the well-known concept of Haskell-style type classes within the logical framework of Isabelle. So far, axiomatic type classes in Isabelle merely account for the logical aspect as predicates over types, while the operational part is only a convention based on raw overloading. Our more elaborate approach to constructive type classes provides a seamless integration with Isabelle loca...

The Constructive Second Number Class*

The existence of at least a vague distinction between what I shall call the constructive and the non-constructive ordinals of the second number class, that is, between the ordinals which can in some sense be effectively built up to step by step from below and those for which this cannot be done (although there may be existence proofs), is, I believe, somewhat generally recognized. My purpose he...

Transfinite Equations in Transfinite Strings