Is it true that the following definitions of completeness are equivalent?(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\mbox{For theory } \Sigma \mbox{ and for any sentence } A[/itex].

[itex]\mbox{ Either } \Sigma \vdash A \mbox{ or } \Sigma \vdash \lnot A [/itex]

and

[itex]\mbox{ Either } A \in \Sigma \mbox{ or } (\lnot A) \in \Sigma[/itex].

(The second clearly implies the first.)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Completeness notions in logic

**Physics Forums | Science Articles, Homework Help, Discussion**