 But ensuring categoricity of mathematical theories does not require introducing stronger quantifiers. Another option would be to take the informal concept of algorithmic computability as a primitive notion (Halbach &amp; Horsten 2005; Horsten 2012). A theorem of Tennenbaum states that all first-order models of Peano Arithmetic in which addition and multiplication are computable functions, are isomorphic to each other. Now our operations of addition and multiplication are computable: otherwise we could never have learned these operations. This, then, is another way in which we may be able to isolate the intended models of our principles of arithmetic. Against this account, however, it may be pointed out that it seems that the categoricity of intended models for real analysis, for instance, cannot be ensured in this manner. For computation on models of the principles of real analysis, we do not have a theorem that plays the role of Tennenbaum’s theorem.