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Rudimentary recursion

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for the seminar given at the University of Birmingham on June 21st 2019 by A. R. D. Mathias, Sc. D. (Cantab), Professeur émérite, LIM , Université de la Réunion

[HMF] H. M. Friedman, Countable Models of Set Theories, in Cambridge Summer School in Mathematical Logic, August 1–21, 1971, edited by A. R. D. Mathias and Hartley Rogers Jr., Springer Lecture Notes in Mathematics 337 (1973) 539–573.

[Slim] A. R. D. Mathias, Slim models of Zermelo set theory, Journal of Sym- bolic Logic 66 (2001) pp 487–496.

[Strong] A. R. D. Mathias, The Strength of Mac Lane Set Theory, Annals of Pure and Applied Logic 110 (2001) pp 107–234.

[Weak] A. R. D. Mathias, Weak systems of Gandy, Jensen and Devlin, in: Set Theory: Centre de Recerca Matemàtica, Barcelona 2003-4, Trends in Mathematics, Birkhäuser, Basel, 2006, pp 149–224.

[Brussels] A. R. D. Mathias, Set forcing over models of Zermelo or Mac Lane, in: One hundred years of axiomatic Set Theory, Cahiers du Centre de logique 17, Academia-Bruylant, Louvain-la-Neuve, 2010, pp 41–66.

[RuGent] A. R. D. Mathias and N.J.Bowler, Rudimentary recursion, gentle func- tions and provident sets, Notre Dame Journal of Formal Logic 56 (2015) pp 3–60.

[ProFor] A. R. D. Mathias, Provident sets and rudimentary set forcing, Funda- menta Mathematicæ 230 (2015) pp 99–148.

[EKMcK] Ali Enayat, Matt Kaufmann, Zachiri McKenzie, Largest initial seg- ments pointwise fixed by automorphisms of models of set theory, Arch. Math. logic 57 (2018) pp 91–139.

[ZMcK] Zachiri McKenzie, On the relative strengths of fragments of collection, Math. Log. Quart 65 (2019) pp 80-94.

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