This is an archived version pinned as of the submission of my master's thesis. An up-to-date version may be found online.

The limited principle of omniscience

module foundation.limited-principle-of-omniscience where
Imports 
open import elementary-number-theory.natural-numbers

open import foundation.disjunction
open import foundation.existential-quantification
open import foundation.universal-quantification
open import foundation.universe-levels

open import foundation-core.identity-types
open import foundation-core.propositions
open import foundation-core.sets

open import univalent-combinatorics.standard-finite-types

Statement

The limited principle of omniscience (LPO) asserts that for every sequence f : ℕ → Fin 2 there either exists an n such that f n ＝ 1 or for all n we have f n ＝ 0.

LPO : UU lzero
LPO =
  (f : ℕ → Fin 2) →
  type-disjunction-Prop
    ( ∃ ℕ (λ n → Id-Prop (Fin-Set 2) (f n) (one-Fin 1)))
    ( ∀' ℕ (λ n → Id-Prop (Fin-Set 2) (f n) (zero-Fin 1)))

See also