THE STRENGTH OF ABSTRACTION WITH PREDICATIVE COMPREHENSION
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AbstractFrege’s theorem says that second-order Peano arithmetic is interpretable in Hume’s Principle and full impredicative comprehension. Hume’s Principle is one example of anabstraction principle, while another paradigmatic example is Basic Law V from Frege’sGrundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence relations in a weak background second-order logic. We show that this predicative Fregean theory interprets second-order Peano arithmetic (cf. Theorem 3.2).
2004 ◽
Vol 10
(2)
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pp. 153-174
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2008 ◽
Vol 18
(2-3)
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pp. 229-246
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2018 ◽
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