Models for Metamath
Abstract
Although some work has been done on the metamathematics of Metamath, there has not been a clear definition of a model for a Metamath formal system. We define the collection of models of an arbitrary Metamath formal system, both for treebased and stringbased representations. This definition is demonstrated with examples for propositional calculus, $\textsf{ZFC}$ set theory with classes, and Hofstadter's MIU system, with applications for proving that statements are not provable, showing consistency of the main Metamath database (assuming $\textsf{ZFC}$ has a model), developing new independence proofs, and proving a form of Gödel's completeness theorem.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 DOI:
 10.48550/arXiv.1601.07699
 arXiv:
 arXiv:1601.07699
 Bibcode:
 2016arXiv160107699C
 Keywords:

 Mathematics  Logic;
 Computer Science  Logic in Computer Science;
 03C95 (Primary);
 03B22;
 03B70 (Secondary);
 F.4.1;
 I.2.3
 EPrint:
 15 pages, 0 figures