Abstract
Certain periods of life look as if they will last for ever. Then suddenly one is struck by the realization that time has gone by and that the period in question has become part of the past. Over 30 years have passed since Per Martin-Löf first came to Padua to give a course on his type theory.
This paper is based on the transcription of my actual talk at the conference Philosophy and Foundations of Mathematics: Epistemological and Ontological Aspects, dedicated to Per Martin-Löf on the occasion of his retirement, Uppsala, May 5–8, 2009, except for the last section, which is also based on my talk at Leeds Symposium on Proof Theory and Constructivism, Leeds (UK), 3–16 July 2009 and on Sambin (2011). I am grateful to John L. Bell and Milly Maietti for useful discussions, to John also for amending my abuses of English and to the editors for their patience with me.
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- 1.
The usual terms to denote inference rules, namely introduction and elimination, would be highly confusing in this context.
- 2.
This option is in common with some foundational theories by Solomon Feferman (1979).
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Sambin, G. (2012). Real and Ideal in Constructive Mathematics. In: Dybjer, P., Lindström, S., Palmgren, E., Sundholm, G. (eds) Epistemology versus Ontology. Logic, Epistemology, and the Unity of Science, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4435-6_4
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