Reference : Implicit dynamic function introduction and Ackermann-like Function Theory
Scientific journals : Article
Arts & humanities : Philosophy & ethics
Implicit dynamic function introduction and Ackermann-like Function Theory
Cramer, Marcos mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
IfCoLog Journal of Logics and Their Applications
[en] We discuss a feature of the natural language of mathematics – the implicit
dynamic introduction of functions – that has, to our knowledge, not been
captured in any formal system so far. If this feature is used without limitations,
it yields a paradox analogous to Russell’s paradox. Hence any formalism
capturing it has to impose some limitations on it. We sketch two formalisms,
both extensions of Dynamic Predicate Logic, that innovatively do capture
this feature, and that differ only in the limitations they impose onto it.
One of these systems is based on Ackermann-like Function Theory, a novel
foundational theory of functions that is inspired by Ackermann Set Theory
and that interprets ZFC.

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