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03-XX Mathematical logic and foundations
03Fxx Proof theory and constructive mathematics
03F40 Gödel numberings and issues of incompleteness

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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.

Currently displaying 1 – 2 of 2

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