most recent 30 from http://mathoverflow.net 2013-05-19T10:55:23Z http://mathoverflow.net/feeds/question/58845 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58845/equivalence-of-monadic-axioms Levon 2011-03-18T15:12:37Z 2011-03-18T16:41:34Z

<p>Call two axioms equivalent if they imply the same set of theorems. I am interested in decidability of so defined equivalence. In this generality the problem is obviously undecidable since it can be used to decide Entscheidungsproblem. So I am interested in cases where Entscheidungsproblem is decidable, particularly in case of monadic axioms (i.e. axioms containing only monadic functional and predicate symbols).</p> <p>Any information about this would be appreciated.</p> <p>Thank you for your time, Levon</p>

http://mathoverflow.net/questions/58845/equivalence-of-monadic-axioms/58853#58853 David Harris 2011-03-18T16:41:34Z 2011-03-18T16:41:34Z

<p>The comment showed that decidability of axiom equivalence is implied by decidability of pure logic. (I.e. to decide if $\Theta$ and $\Theta'$ are equivalent, it is equivalent to decide if $\vdash \Theta \leftrightarrow \Theta'$. Conversely, if one can decide axiom equivalence, then one can decide pure logic. Namely, $\vdash \Theta$ iff the axiom $\Theta$ is equivalent to $\top$.</p>