Mathematical Logic Well-foundedness in realizability
نویسندگان
چکیده
However, the implication from (1) to (2) is equivalent to the principle of dependent choices (as the reader can show for himself) and cannot be proved in ZF. A relation < on X is called well-founded if any of these statements holds. Intuitionistically, the three statements are far from equivalent (hence, in formalizing an intuitionistic notion of well-foundedness, care is needed). Notion (1) is, intuitionistically, too weak to be of any use; in contrast, notion (2) is
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