I started reading a Mathematical logic book.I wondered what is a definition by abstraction as well axiom schemata.
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Axiom schemata is a phrase used for an axiom that's really many axioms in one. Typically countably infinitely many axioms. For instance, if the axiom says "for any formula $\phi$...", then really, it's one separate axiom for each formula $\phi$. Therefore, since such a statement is not strictly an axiom, it's called an axiom schemata. – Arthur Aug 04 '15 at 23:56
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what you mean by countably infinitely? – Bill Aug 05 '15 at 00:01
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Perhaps I just meant "countably many". I just don't feel that that phrase rules out "finitely many", as in "the number is countably infinite", so I said "countably infinitely many". It's late, I'm sorry for the confusion. – Arthur Aug 05 '15 at 00:21
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no worry. Thanks. – Bill Aug 05 '15 at 00:48