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\documentclass{book}
\usepackage[colorlinks]{hyperref}
\begin{document}

{\bf Intuitionistic Propositional Logic For Children and
  Meta-Children, or: How Archetypal Are Finite Planar Heyting
  Algebras?}

\medskip

I've been using the expression ``for children'' in titles for some
years, and with time it acquired a precise, though unusual, sense.
``Children'' are ``people without mathematical maturity'', where these
are the main aspects of mathematical maturity: ableness to 1) handle
abstract mathematical structures and 2) infinite objects; 3) work
axiomatically, 4) generalize, and 5) particularize.

Some techniques for creating versions ``for children'' of maths ``for
adults'' are described in [1]; the main one is doing two parallel
diagrams, one for the general case and another one for a particular,
hopefully ``archetypal'' case.

Finite, planar Heyting Algebras (``ZHA''s) are very good tools for
teaching Intuitionistic Propositional Logic (IPL) to children: most
non-theorems of IPL have countermodels on ZHAs that are very easy to
understand visually, and children prefer to understand tautologies and
non-tautologies first, and deductive systems later.

ZHAs are archetypal among Heyting Algebras, but in a sense of
``archetypal'' that fits only the loosest definitions in [1], sec.16.

``Meta-children'' are people who want to study the relation between
mathematics ``for children'' and ``for adults'' and produce
(meta)mathematics for adults from that. The presentation will be
mostly about teaching ZHAs and closure operators to ``children'', with
one result for meta-children in the end: that this new sense of
archetypalness can be formalized using comparisons of partial orders
([2], last sections).

\bigskip

[1]: Ochs, E.: {\sl Internal Diagrams and Archetypal Reasoning in
  Category Theory}. Logica Universalis, 2013.

[2]: Ochs, E: {\sl Intuitionistic Logic for Children, or: Planar
  Heyting Algebras for Children}. Preprint, 2017.

\medskip

Eduardo Ochs --- UFF

eduardoochs@gmail.com

Home page: \url{http://angg.twu.net/math-b.html}

\end{document}





% this: let D be the diagram for the partial order on positive
% modalities in S4 from Chellas's {\sl Modal Logic}, p.149; let
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% ``archetypal'' somewhat different from [1], that fits only the loose
% definition in sec.16.


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