extensions of monadic first order logic
in [Logic]
|
Prev: math symbols in unicode (grouped by purpose)
Next: PRENTICE HALL'S FEDERAL TAXATION: 2011 INDIVIDUALS THOMAS R. POPEKENNETH E. ANDERSON JOHN L. KRAMER SOLUTION MANUAL
From: jmc12 on 13 Aug 2010 18:14 As is well known,monadic first order logic is not post-complete---it has consistent proper extensions. For example the formula (1) ExFx ---> AxFx could be added as an axiom schema without resulting in inconsistency (its valid in the class of models with a singletom domain). I was wondered, if there was a paper where anyone has proved some results about logics which extend monadic FOL? Eg. do ALL of its extensions involve 'counting' formulas like (1)? thanks in adavance for any help.
From: herbzet on 13 Aug 2010 20:40 jmc12 wrote: > > As is well known,monadic first order logic is not post-complete---it > has consistent proper extensions. For example the formula > > (1) ExFx ---> AxFx > > could be added as an axiom schema without resulting in inconsistency > (its valid in the class of models with a singletom domain). > > I was wondered, if there was a paper where anyone has proved some > results about logics which extend monadic FOL? Eg. do ALL of its > extensions involve 'counting' formulas like (1)? > > thanks in adavance for any help. By extensions, you mean adding new axioms, like (1), without extending the language by adding, say, 2-place predicate symbols? You're interested in whether any consistent new axiom in the same language will necessarily limit the size of the domain? -- hz
From: jmc12 on 13 Aug 2010 21:00
On Aug 14, 1:40 am, herbzet <herb...(a)gmail.com> wrote: > jmc12 wrote: > > > As is well known,monadic first order logic is not post-complete---it > > has consistent proper extensions. For example the formula > > > (1) ExFx ---> AxFx > > > could be added as an axiom schema without resulting in inconsistency > > (its valid in the class of models with a singletom domain). > > > I was wondered, if there was a paper where anyone has proved some > > results about logics which extend monadic FOL? Eg. do ALL of its > > extensions involve 'counting' formulas like (1)? > > > thanks in adavance for any help. > > By extensions, you mean adding new axioms, like (1), without > extending the language by adding, say, 2-place predicate > symbols? > > You're interested in whether any consistent new axiom in > the same language will necessarily limit the size of the > domain? > > -- > hz yes. sorry i should have been more clear---i mean extensions of the logic (more theorems), rather than extensions of the language. i suppose i'm just interested in what (consistent) extensions there are in general. those that if added as an axiom to FOL will limit the size of the domian (such as the formula (1)) are the only ones i can think of, but perhaps there are more. |