Introduction to the Foundations of Mathematics

a₁ algebra arithmetic axiom system axiomatic method binary relation Brouwer calculus called Cantor cardinal number Chapter Choice Axiom collection concept consider consistency contains contradiction Corollary corresponding countable course culture Dedekind infinite defined definition denote denumerable digits elements of F equivalence relation euclidean geometry example exists a 1-1)-correspondence finite sets follows formula function given Gödel hence Hilbert implies infinite set instance integers intuitionist isomorphic L₁ latter Lemma logic M₁ mathe mathematical induction mathematicians matics mean ments natural numbers non-empty notion order type ordinal ordinary infinite pair Peano Peano axioms points postulates Problem proof proper subset propositions prove r₁ r₂ rational numbers reader real number system respect S₁ satisfy sequence Sierpinski S1 simply ordered set statement symbols system of axioms theory tion transfinite induction undefined terms w₁ well-ordered set Well-ordering Theorem zero