Weak Systems of Gandy, Jensen and Devlin

3 0 Introduction 3 Part I 1 Formulation of the various systems 7 2 Theorems of various systems 13 On ReS and finite sets 13 Proof that HF models ZF – Infinity 16 On GJ and the class of rudimentary functions 20 Companions and the Gandy–Jensen Lemma 21 A single generating function for rud(u) 22 Other remarks on GJ 23 On fReR 25 On ReRI 26 On KP 27 3 Remarks on transitive models 27 4 Models of ReS 30 A model of ReS with full separation omitting [ω] and [ω] 31 5 Models of DB 33 A model of DB omitting [ω] 35 A failure of ⋃ “ 36 A failure of Seq 37 6 Models of GJ 38 7 Models of fReR and beyond 39 A class model of Z + TCo omitting most ordinals 39 ∗ Centre de Recerca Matemàtica, Bellaterra, Catalonia and ERMIT, Université de la