Cambridge Summer School in Mathematical Logic

3x Ax A₁ admissible ordinals admissible set algorithm Amsterdam analog computer applications arithmetic assigned assume atomic axiom of choice B)-formula B)-terms ball C₁ choice sequences classical closed conservative extension consistent constant construction Corollary countable defined definition denote dense disjunction equivalent exists extensionality finite formula given Hence Heyting hole implies induction infinite initial segment interpretation Intuitionism intuitionistic Kleene Kreisel lawlike Lemma Let f level zero logic MAHLO's Math mathematics measurable cardinal natural numbers nonstandard normal form notion obtained ordinal parameters partition power admissible set Prawitz predicate primitive recursive principle proof proof theory Proposition provable prove Ramsey's theorem realizability recursion theory recursive function relation rules satisfying second order sentence set theory sort soundness theorem species subset Suppose symbols T₁ T₂ term Troelstra 1971 ultrafilter variables