   In constructive analysis It is equivalent, in the language of real analysis, to the following principles: Realizability If constructive arithmetic is translated using realizability into a classical meta-theory that proves the -
<meaning-changed>    In constructive analysis It is equivalent, in the language of real analysis, to the following principles: Realizability If constructive arithmetic is translated using realizability into a classical meta-theory that proves the -
 If instead the realizability interpretation is used in a constructive meta-theory, then it is not justified. Indeed, for first-order arithmetic, Markov's principle exactly captures the difference between a constructive and classical meta-theory. Specifically, a statement is provable in Heyting arithmetic with Extended Church's thesis if and only if there is a number that provably realizes it in Heyting arithmetic; and it is provable in Heyting arithmetic with Extended Church's thesis and Markov's principle if and only if there is a number that provably realizes it in Peano arithmetic. In constructive analysis It is equivalent, in the language of real analysis, to the following principles: Realizability If constructive arithmetic is translated using realizability into a classical meta-theory that proves the -