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Predicative Mathematics in Type Theory Robin Adams
 

Summary: Predicative Mathematics in Type Theory
Robin Adams
July 20, 2005
1 Introduction
We present a weak, logic-enriched type theory intended for the formalization
of predicative mathematics in the style of Weyl's "Das Kontinuum". We show
how the results stated and proved in "Das Kontinuum" would be formalized in
such a system.
1. Differences between this system and Weyl:
We allow (through EN) the definition of functions by recursion. Weyl
must define these as predicates in quite a complicated manner.
We start the natural numbers at 0, rather than 1. We follow the
order of progression
N Z Q
rather than Weyl's
N Q+
Q
This requires quite a lot of change in the detail in the parts dealing
with Z and Q.
We use function types A B rather than functions as graphs or as

  

Source: Adams, Robin - Department of Computer Science, Royal Holloway, University of London

 

Collections: Computer Technologies and Information Sciences