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Normalization Theorems for the Intuitionistic Systems with Choice Principles

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Mathematical Logic

Abstract

We review here some intuitionistic systems with choice principles

$$\forall x\left( {Ey} \right)A\left( {x,y} \right) \to \left( {Ef} \right)\forall xA\left( {x,f\left( x \right)} \right)$$
(1)

for which normalization theorems have been established. These are mainly first order systems or systems close to the first order ones in their deductive power. This is not accidental, since in higher order intuitionistic logic with extensionality choice seems to imply excluded third [1].

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Authors and Affiliations

  1. Institute of Cybernetics, Estonian Academy of Sciences, 200108, Tallinn, USSR

    Grigorii Mints

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  1. Grigorii Mints
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Editor information

Editors and Affiliations

  1. Sofia University, Sofia, Bulgaria

    Petio Petrov Petkov

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© 1990 Plenum Press, New York

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Mints, G. (1990). Normalization Theorems for the Intuitionistic Systems with Choice Principles. In: Petkov, P.P. (eds) Mathematical Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0609-2_6

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  • DOI: https://doi.org/10.1007/978-1-4613-0609-2_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-7890-0

  • Online ISBN: 978-1-4613-0609-2

  • eBook Packages: Springer Book Archive

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