Index: CSL17/DICE2017_TALK/survey_light_Shonan copie.toc
===================================================================
--- CSL17/DICE2017_TALK/survey_light_Shonan copie.toc	(revision 189)
+++ CSL17/DICE2017_TALK/survey_light_Shonan copie.toc	(revision 190)
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Index: CSL17/DICE2017_TALK/unboundedArithmetic.nav
===================================================================
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Index: CSL17/DICE2017_TALK/unboundedArithmetic.toc
===================================================================
--- CSL17/DICE2017_TALK/unboundedArithmetic.toc	(revision 189)
+++ CSL17/DICE2017_TALK/unboundedArithmetic.toc	(revision 190)
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Index: CSL17/DICE2017_TALK/unboundedArithmetic.pdf
===================================================================
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Index: CSL17/DICE2017_TALK/unboundedArithmetic.synctex.gz
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Index: CSL17/DICE2017_TALK/unboundedArithmetic.aux
===================================================================
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Index: CSL17/DICE2017_TALK/unboundedArithmetic.log
===================================================================
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Index: CSL17/DICE2017_TALK/unboundedArithmetic.tex
===================================================================
--- CSL17/DICE2017_TALK/unboundedArithmetic.tex	(revision 189)
+++ CSL17/DICE2017_TALK/unboundedArithmetic.tex	(revision 190)
@@ -211,6 +211,25 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
+  \frametitle{Ramification}
+ 
+ \begin{itemize}
+\item   ramification, a.k.a. tiering, safe recursion
+\item distinguish two levels of data-types:
+
+${\red{N_1}}$ (\textit{normal}) integers can trigger induction/recursion
+
+${{N_0}}$ (\textit{safe})  integers cannot; they can just be finitely explored
+\item ramified recursion scheme:
+$$ f({\red{\succ{i} u, \vec v}}{\textbf ;} \vec x)=F_i ({\red{u,\vec v}}{\textbf ; }f(u, \vec v;\vec x), \vec x)$$
+\item function algebra for FP: Bellantoni-Cook 92, Leivant 93
+
+          logic for FP: Leivant 95, Cantini 00 
+\end{itemize}
+ \end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
   \frametitle{Ingredients for a logical characterization}
  
  \begin{itemize}
