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  1. History and Philosophy of Constructive Type Theory.Giovanni Sommaruga - 2000 - Dordrecht, Netherland: Springer.
    A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. (...)
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  • Extensionality Versus Constructivity.Silvio Valentini - 2002 - Mathematical Logic Quarterly 48 (2):179-187.
    We analyze some extensions of Martin-Löf 's constructive type theory by means of extensional set constructors and we show that often the most natural requirements over them lead to classical logic or even to inconsistency.
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  • Can You Add Power‐Sets to Martin‐Lof's Intuitionistic Set Theory?Maria Emilia Maietti & Silvio Valentini - 1999 - Mathematical Logic Quarterly 45 (4):521-532.
    In this paper we analyze an extension of Martin-Löf s intensional set theory by means of a set contructor P such that the elements of P are the subsets of the set S. Since it seems natural to require some kind of extensionality on the equality among subsets, it turns out that such an extension cannot be constructive. In fact we will prove that this extension is classic, that is “ true holds for any proposition A.
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  • Proceeding in Abstraction. From Concepts to Types and the Recent Perspective on Information.Giuseppe Primiero - 2009 - History and Philosophy of Logic 30 (3):257-282.
    This article presents an historical and conceptual overview on different approaches to logical abstraction. Two main trends concerning abstraction in the history of logic are highlighted, starting from the logical notions of concept and function. This analysis strictly relates to the philosophical discussion on the nature of abstract objects. I develop this issue further with respect to the procedure of abstraction involved by (typed) λ-systems, focusing on the crucial change about meaning and predicability. In particular, the analysis of the nature (...)
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