Introduction to the Foundations of Mathematics

algebra arithmetic assertion axiom system axiomatic method basic basis binary relation Brouwer calculus called Cantor cardinal number Chapter Choice Axiom concept consider consistency contradiction Corollary corresponding countable course culture decimal Dedekind infinite defined definition denote denumerable digits discussion elements of F equivalence relation euclidean geometry example Excluded Middle exists a 1-1)-correspondence follows formal formula given Gödel hence Hilbert implies induction principle infinite set instance integers interpretation intuitionist isomorphic L₁ latter Lemma line contains logic M₁ mathe mathematical induction mathematicians matics mean ment natural numbers notion order type ordinal ordinary pair Peano Peano axioms plane geometry point and line postulates Problem proof propositional functions r₁ rational numbers reader S₁ satisfy sequence Sierpinski simply ordered set species statement symbols system of axioms theory tion transfinite induction undefined terms variables w₁ well-ordered set Well-ordering Theorem