We characterize categories whose internal logic is Hilbert's ε-calculus as those categories which have a proper factorization system satisfying the axiom of choice and in which every non-initial object is injective. We provide an example of such a category where the law of excluded middle is not valid.
A characterization of those categories whose internal logic is Hilbert's ε-calculus / F. Pasquali. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 170:4(2019 Apr), pp. 446-464. [10.1016/j.apal.2018.11.003]
A characterization of those categories whose internal logic is Hilbert's ε-calculus
F. Pasquali
2019
Abstract
We characterize categories whose internal logic is Hilbert's ε-calculus as those categories which have a proper factorization system satisfying the axiom of choice and in which every non-initial object is injective. We provide an example of such a category where the law of excluded middle is not valid.
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