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Jan 8, 2010 at 15:19 comment added Hans-Peter Stricker Rather advanced, but thanks.
Jan 8, 2010 at 15:13 comment added SixWingedSeraph Read about sketches in Johnstone's book Sketches of an Elephant (second volume). They give a hierarchy going down from your number (1) -- geometric logic, essentially algebraic logic (finite-limit theories), algebraic logic. There are many variations. There is undoubtedly no end to such classifications, both up and down from first order logic.
Jan 8, 2010 at 14:42 history edited Hans-Peter Stricker CC BY-SA 2.5
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Jan 8, 2010 at 14:30 history asked Hans-Peter Stricker CC BY-SA 2.5