Basic first-order model theory in Mizar

The author has submitted to Mizar Mathematical Library a series of five articles introducing a framework for the formalization of classical first-order model theory.In them, Goedel's completeness and Lowenheim-Skolem theorems have also been formalized for the countable case, to offer a first ap...

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Main Author: Marco Bright Caminati
Format: Article
Language:English
Published: University of Bologna 2010-01-01
Series:Journal of Formalized Reasoning
Online Access:http://jfr.cib.unibo.it/article/view/1974/1361
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spelling doaj-06c6865a582646dc8a21696f44e664292020-11-24T22:24:36ZengUniversity of BolognaJournal of Formalized Reasoning1972-57872010-01-01314977Basic first-order model theory in MizarMarco Bright CaminatiThe author has submitted to Mizar Mathematical Library a series of five articles introducing a framework for the formalization of classical first-order model theory.In them, Goedel's completeness and Lowenheim-Skolem theorems have also been formalized for the countable case, to offer a first application of it and to showcase its utility.This is an overview and commentary on some key aspects of this setup.It features exposition and discussion of a new encoding of basic definitions and theoretical gears needed for the task, remarks about the design strategies and approaches adopted in their implementation, and more general reflections about proof checking induced by the work done.http://jfr.cib.unibo.it/article/view/1974/1361
collection DOAJ
language English
format Article
sources DOAJ
author Marco Bright Caminati
spellingShingle Marco Bright Caminati
Basic first-order model theory in Mizar
Journal of Formalized Reasoning
author_facet Marco Bright Caminati
author_sort Marco Bright Caminati
title Basic first-order model theory in Mizar
title_short Basic first-order model theory in Mizar
title_full Basic first-order model theory in Mizar
title_fullStr Basic first-order model theory in Mizar
title_full_unstemmed Basic first-order model theory in Mizar
title_sort basic first-order model theory in mizar
publisher University of Bologna
series Journal of Formalized Reasoning
issn 1972-5787
publishDate 2010-01-01
description The author has submitted to Mizar Mathematical Library a series of five articles introducing a framework for the formalization of classical first-order model theory.In them, Goedel's completeness and Lowenheim-Skolem theorems have also been formalized for the countable case, to offer a first application of it and to showcase its utility.This is an overview and commentary on some key aspects of this setup.It features exposition and discussion of a new encoding of basic definitions and theoretical gears needed for the task, remarks about the design strategies and approaches adopted in their implementation, and more general reflections about proof checking induced by the work done.
url http://jfr.cib.unibo.it/article/view/1974/1361
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