Impact
~3k
people reached
- 0 posts edited
- 0 helpful flags
- 6 votes cast
Mar
30 |
comment |
Question on Godel completeness theorem
@Henry Cohn Thanks! Statement "Consistent theory T" has a clear substantial sense and it means that on any step of the proof we cannot prove the formula 1=0. But construction of proofs is real physical process and for example, if "10 ^ {10 ^ {10000} exists" has not the same substantial sense as well as "2 exists" then and statement Con (T) obviously has not any sense. |
Mar
29 |
comment |
Question on Godel completeness theorem
> I really think that "is $T $ consistent?" and "what do symbols mean?" are unrelated.) $T $ consistent has clear substantial sense and it means that on any step of the proof we cannot prove the formula 1=0. But construction of proofs is real physical process and if "10 ^ {10 ^ {10000} exists" has not the same substantial sense as well as "2 exists" then and statement Con (T) has not any sense. |
Mar
29 |
comment |
Question on Godel completeness theorem
Well. Then explain to me that you particularly mean when tell that number $10 ^ {10 ^ {10000}} $ exist. It something real or only a symbol? |
Mar
29 |
comment |
Question on Godel completeness theorem
Noah > In particular, can you please explain what you mean by "really exists?" "Really exists" means exist as real infinite physical object or infinite physical process. For example E.Nelson in fact asserts that such object or process does not exist, i.e. РА has no any standard models. |
Mar
28 |
comment |
Question on Godel completeness theorem
> then at some level you must be rejecting infinite sets, which is fine, In it there is no necessity. Nevertheless it is possible to assume that real-life infinite sets, are not obliged to correspond to the classical logic. |
Mar
28 |
comment |
Question on Godel completeness theorem
Andrej Bauer. >but "really exist" might mean "exists constructively". Well. Thus "really exist" completely depend on logic. |
Mar
26 |
comment |
Question on Godel completeness theorem
>Let me elaborate a bit on why having computationally simple models >is relevant. It's not just that such models are "less complicated" >than standard set-theoretic constructions, as I state above; it's >that we don't even need to talk about set theory, at all, to get >them! The models in question are uniformly It agree.But nevertheless there are known mathematicians which think that such constructive process will suffer contradictions web.math.princeton.edu/~nelson/papers/warn.pdf |
Mar
26 |
accepted | Question on Godel completeness theorem |
Mar
26 |
asked | Question on Godel completeness theorem |
Mar
22 |
comment |
Standard model of ZFC
Noah S. You rave. My question is put clearly and no any relation to my statements in other places has. Moreover I never addressed to whom or with intentions to check my proofs and the more so their sketches. |
Mar
17 |
accepted | Standard model of ZFC |
Mar
17 |
awarded | Commentator |
Mar
17 |
comment |
Standard model of ZFC
Joel David Hamkins.Yes of course. |
Mar
16 |
comment |
Standard model of ZFC
I'm asking does it follow from ZFC+ there exists some model of ZFC |
Mar
16 |
comment |
Standard model of ZFC
Timothy Chow >What you're asking is, as long as there exists some model of ZFC, does it follow that no models are standard? Yes of course. |
Mar
16 |
revised |
Standard model of ZFC
added 9 characters in body |
Mar
16 |
revised |
Standard model of ZFC
added 29 characters in body |
Mar
16 |
asked | Standard model of ZFC |
Mar
7 |
awarded | Scholar |
Mar
7 |
accepted | Reflection principles |