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The Justification of Identity Elimination in Martin-Löf’s Type Theory

  • Ansten KlevEmail author


On the basis of Martin-Löf’s meaning explanations for his type theory a detailed justification is offered of the rule of identity elimination. Brief discussions are thereafter offered of how the univalence axiom fares with respect to these meaning explanations and of some recent work on identity in type theory by Ladyman and Presnell.


Justification of logical laws Type theory Identity 



I am grateful to Göran Sundholm for many discussions on the philosophical foundations of type theory and to Per Martin-Löf, who in correspondence clarified what is the canonical form of an element of an Id-set. The comments of two referees at Topoi were of great help when preparing the final version of the paper. Thanks are also due to the referees of a predecessor of this paper that was submitted to another journal. While writing the paper, the author has been supported by Grant No. 17-18344Y from the Czech Science Foundation, GAČR.


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Logic, Institute of Philosophy, Czech Academy of SciencesPraha 1Czech Republic

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