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Book Sections Year : 2021

On Measure Quantifiers in First-Order Arithmetic


We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all possible interpretations of the quantified variable. We show that first-order arithmetic with measure quantifiers is capable of formalizing simple results from probability theory and, most importantly, of representing every recursive random function. Moreover, we introduce a realizability interpretation of this logic in which programs have access to an oracle from the Cantor space.
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Dates and versions

hal-03346804 , version 1 (20-09-2021)



Melissa Antonelli, Ugo Dal Lago, Paolo Pistone. On Measure Quantifiers in First-Order Arithmetic. Proceedings of CIE 2021, pp.12-24, 2021, ⟨10.1007/978-3-030-80049-9_2⟩. ⟨hal-03346804⟩
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