Abstract
We generalize a well-knownSmullyan's result, by showing that any two sets of the kindC a = {x/⊢ x↔a} andC b = {x/⊢ x↔b} are effectively inseparable (if I ⌿ ↔b). Then we investigate logical and recursive consequences of this fact (see Introduction).
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Bernardi, C. On the relation provable equivalence and on partitions in effectively inseparable sets. Stud Logica 40, 29–37 (1981). https://doi.org/10.1007/BF01837553
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DOI: https://doi.org/10.1007/BF01837553