Normalization Theorems for the Intuitionistic Systems with Choice Principles

Grigorii Mints
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Grigorii Mints: Estonian Academy of Sciences, Institute of Cybernetics

A chapter in Mathematical Logic, 1990, pp 59-66 from Springer

Abstract: Abstract We review here some intuitionistic systems with choice principles 1 $$\forall x\left( {Ey} \right)A\left( {x,y} \right) \to \left( {Ef} \right)\forall xA\left( {x,f\left( x \right)} \right)$$ 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].

Keywords: Finite Type; Predicate Calculus; Natural Deduction; Normalization Theorem; Transfinite Induction (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-1-4613-0609-2_6

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