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The Gödel Completeness Theorem for Uncountable Languages

Julian J. Schlöder;  Peter Koepke — 2012

Formalized Mathematics

This article is the second in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [15] for uncountably large languages. We follow the proof given in [16]. The present article contains the techniques required to expand a theory such that the expanded theory contains witnesses and is negation faithful. Then the completeness theorem follows immediately.

Transition of Consistency and Satisfiability under Language Extensions

Julian J. Schlöder;  Peter Koepke — 2012

Formalized Mathematics

This article is the first in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [17] for uncountably large languages. We follow the proof given in [18]. The present article contains the techniques required to expand formal languages. We prove that consistent or satisfiable theories retain these properties under changes to the language they are formulated in.

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