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I have a proposal for a new comprehension scheme for second order
logic:
Let w be an arbitrary equivalence relation (by which I do not mean a
second-order entity, since then this comprehension scheme would be
circular. Instead, I mean a wff with two free variables that is
reflexive, transitive, and symmetric). Then for all x, there exists an
F such that for all y, Fy iff w(x,y).
How does this comprehension schema compare with the regular
comprehension schema of second-order logic?
Any help would be greatly appreciated.
Thank You in Advance.
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