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\begin{document}

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\section*{Practical Foundations of Mathematics}

The book

\begin{itemize}%
\item [[Paul Taylor]], \emph{Practical Foundations of Mathematics} (\href{http://www.paultaylor.eu/~pt/prafm/index.html}{web})

\end{itemize}
is a description of how (in Taylor's opinion) the [[foundations]] of mathematics should really be done, with an eye towards matching how mathematics is done in practice (with the consequence that the system is no stronger than necessary).

The result is actually a series of foundations, most [[constructive mathematics|constructive]], suitable for different sorts of mathematics. Ultimately, these are described as [[internal logic|logic in]] categories defined by [[sketch]]es and equipped with distinguished [[pullback]]-stable classes of \emph{display morphisms}.

It is \href{http://www.PaulTaylor.EU/Practical-Foundations/index.html}{available online} in a somewhat unreadable format.

A useful survey of some of the topics discussed there is also in

\begin{itemize}%
\item [[Paul Taylor]], \emph{Foundations for computable topology} (\href{http://www.paultaylor.eu/ASD/foufct/abstract.html}{web})

\end{itemize}
which is an exposition of Taylor's [[Abstract Stone Duality]].

\hypertarget{related_entries}{}\subsection*{{Related entries}}\label{related_entries}

\begin{itemize}%
\item [[Robert Harper]],

\emph{[[Practical Foundations for Programming Languages]]},

Cambridge University Press (2016), (\href{http://www.cambridge.org/us/academic/subjects/computer-science/programming-languages-and-applied-logic/practical-foundations-programming-languages-2nd-edition?format=HB}{webpage})


\item [[William Lawvere]], [[Robert Rosebrugh]],

\emph{[[Sets for Mathematics]]},

Cambridge UP 2003 (\href{http://www.mta.ca/~rrosebru/setsformath/}{book homepage}, \href{http://books.google.de/books?id=h3_7aZz9ZMoC&pg=PP1&dq=sets+for+mathematics}{GoogleBooks}, \href{http://patryshev.com/books/Sets%20for%20Mathematics.pdf}{pdf})



\end{itemize}
category: reference

[[!redirects Practical Foundations]] [[!redirects Practical Foundations of Mathematics]] [[!redirects PFM]]



\end{document}