“Markov’s principle”的概念、定义、翻译、参考文献-科学参考

Markov’s principle

Logic

A restricted axiom scheme in the language of arithmetic due to mathematician Andrei Markov, Jr. (1903–1979) of the form:
- • $\neg\neg \exists x φ (x) \to \exists x φ (x)$
when $φ (x)$ is decidable. On the BHK interpretation of mathematics, this is read as the statement that whenever the inexistence of a witness for a decidable $φ (x)$ would lead to absurdity, one is able to construct such a witness. Markov’s principle is not valid in Heyting Arithmetic ( $HA$ ), although the rule form of the axiom (Markov’s rule) is admissible in $HA$ .

单词	Markov’s principle
释义	Markov’s principle Logic A restricted axiom scheme in the language of arithmetic due to mathematician Andrei Markov, Jr. (1903–1979) of the form: • $\neg\neg \exists x φ (x) \to \exists x φ (x)$ when $φ (x)$ is decidable. On the BHK interpretation of mathematics, this is read as the statement that whenever the inexistence of a witness for a decidable $φ (x)$ would lead to absurdity, one is able to construct such a witness. Markov’s principle is not valid in Heyting Arithmetic ( $HA$ ), although the rule form of the axiom (Markov’s rule) is admissible in $HA$ .
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