A set thoery based on MV-logic with a universal set?

[phoenixthoth]

OK, so I'm wondering if anyone at PF knows anything about this stuff. This is from my blog so it's kind of not grammatically (or even necessarily mathematically) correct:



well, i dug out some old books for reading. two heavy math books that baffle the **** out of me and two heave spiritual books that baffle the **** out of me. I'm quite pleased, trying to not be "too" pleased, that i am for whatever reason understanding one of the math books i want to get into about many-valued logic. i have an idea for a math phd thesis problem and I'm trying to figure out if it's already been done and, if not, worthy of a phd. i want to determine if there is a set theory with minimal axioms adjusted in which there is a set of all sets, which Cantor likened to God but was proved to be impossible in NOT-many-valued logic by Russell (thus really scaring the crap out of Cantor because he believed this was PROOF that God does not exist), using many-valued logic. for about 70 years now, people know that alternate set theories exist in which there is a universal set (aka a set of all sets) but they come with severe down-sides. what i don't know is whether a theory can be developed in MV-logic (many-valued logic) that has fewer down-sides than the other new set theories that has a universal set. i'd like to answer that question, whether it is yes or no. and if there is a universal set theory based on MV-logic, i want to prove that it is consistent relative to standard set theory; this has NOT been done in the new set theories with a universal set (the ones with the severe drawbacks). [[when i say relative to, i mean something along the lines of "if set theory is consistent THEN my theory is consistent." it is not possible to actually prove standard set theory is consistent by Goedel's incompleteness theorem***, I think. but most people believe it is consistent.]] so if i could find out if someone has done an MV-set theory with a universal set already, then that would pretty much shoot down my only idea even remotely like a phd thesis.


***I'm not sure about this and other points.

 

[Evalesco]

Hi there! It sounds like you have a really interesting research idea that you are considering for a potential PhD thesis. Unfortunately, it's hard to say whether anyone at PF knows anything about this particular topic without knowing more specific details. However, if you are needing help with understanding the mathematics involved, then you can try posting on the Mathematics subforum where you may be able to get some helpful advice from members who are more knowledgeable in the subject. Hope this helps!

 

[tacman]

Hello there! It sounds like you have a very interesting topic for your potential PhD thesis. I am not an expert in many-valued logic or set theory, but I can offer some thoughts on your idea.

Firstly, I am not aware of any set theory based on MV-logic that includes a universal set. However, this does not necessarily mean that your idea is not worthy of a PhD. In fact, the fact that no one has done it before could make it an even more interesting and valuable contribution to the field.

Secondly, I think it is important to carefully define what you mean by a "universal set" in the context of MV-logic. In traditional set theory, the concept of a universal set has been shown to lead to contradictions (as you mentioned with Cantor and Russell). Therefore, it may be necessary to redefine what a universal set means in MV-logic in order to avoid these contradictions.

Lastly, I think it is important to consider the potential drawbacks of your theory, even if it is successful in providing a consistent universal set in MV-logic. As you mentioned, other set theories with a universal set have severe down-sides, so it would be important to address these in your theory and provide evidence for why your theory is a better alternative.

Overall, I think your idea has potential and could definitely be a worthy PhD thesis. I would suggest doing more research and discussing your idea with experts in the field before making a final decision. Good luck!