Introduction to the Foundations of Mathematics

a₁ algebra arithmetic assertion axiom system axiomatic method binary relation Brouwer calculus called Cantor cardinal number Chapter Choice Axiom collection concept consistency contains contradiction Corollary corresponding countable culture Dedekind infinite defined definition denote denumerable digits elementary elements of F equivalence equivalence relation euclidean euclidean geometry example Excluded Middle exists a 1-1)-correspondence follows formula geometry given Gödel hence Hilbert implies infinite sets integers Intuitionism intuitionist isomorphic latter Lemma M₁ Math mathematical induction mathematicians matics mean ment modern natural numbers non-empty notion operation order type ordinal ordinary pair Peano Peano axioms plane probably Problem proof propositional function prove r₁ r₂ rational numbers reader real number system recursive respect S₁ satisfy sequence set theory simply ordered set species statement subset tion topology transfinite induction variables w₁ well-ordered set Well-ordering Theorem zero