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

  1. Aug 20, 2007 #1
    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.
     
  2. jcsd
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