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A note on Mathematics of infinity

Published online by Cambridge University Press:  12 March 2014

Erik Palmgren
Erik Palmgren*
Affiliation:
Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden, E-mail: Erik.Palmgren@math.uu.se
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Extract

In the paper Mathematics of infinity, Martin-Löf extends his intuitionistic type theory with fixed “choice sequences”. The simplest, and most important instance, is given by adding the axioms

to the type of natural numbers. Martin-Löf's type theory can be regarded as an extension of Heyting arithmetic (HA). In this note we state and prove Martin-Löf's main result for this choice sequence, in the simpler setting of HA and other arithmetical theories based on intuitionistic logic (Theorem A). We also record some remarkable properties of the resulting systems; in general, these lack the disjunction property and may or may not have the explicit definability property. Moreover, they represent all recursive functions by terms.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 4 , December 1993 , pp. 1195 - 1200
Copyright
Copyright © Association for Symbolic Logic 1993

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References

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