It is commonly understood that Countable Choice holds constructively due to the underlying computational nature of constructivism. However, in this paper we demonstrate that invoking different notions of computation result in radically different behaviors regarding Countable Choice. In particular, we illustrate that, although deterministic computation guarantees Countable Choice, non-deterministic computation can negate Countable Choice. We then further show that using stateful computation can restore Countable Choice even in the presence of non-determinism. This finding suggests that much of the modern discourse of constructivism assumes a deterministic underlying computational system, despite non-determinism being a fundamental aspect of modern-day computation.
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