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THE THEORY OF SETS
SOME FUNDAMENTAL CONCEPTS
A CRITIQUE OF MATHEMATICAL REASONING
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abbreviation algorithm applied arithmetic assumption formula Axiom Schema axiomatic classical computation contain x free Corollary Theorem corresponding course-of-values decision problem defined distinct variables domain effectively calculable entities enumerable equations equivalent Example f-term finitary formal symbols formal system free variables function 9 function letter function symbol given deduction Godel number Hence Hilbert hypothesis inductive definition inference infinite interpretation intuitionistic system Kleene Lemma logical symbols machine mathematics metamathematical method n-tuple natural numbers notation notion number theory number-theoretic system obtain occur free operation p(xv partial function partial recursive function particular postulates predicate calculus predicate letter formula primitive recursive function proof of Theorem proposition letter formula propositional calculus prove quantifiers real numbers realizes recursive predicate replace representing function respectively result rules of inference satisfied scanned schemata Similarly simply consistent square substitution thesis true Turing machine unprovable V-introd VxA(x