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Questions
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Can a model of set theory be realized as a Cohen-subset forcing extension in two different ways, with different grounds and different cardinals?

feb 1 at 20:57 Joel David Hamkins 74.9k●7●187●343

 
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Can there be a global linear ordering of the universe without a global well-ordering of the universe?

nov 3 at 18:07 Joel David Hamkins 74.9k●7●187●343

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Can there be an embedding j:V to L, from the set-theoretic universe V to the constructible universe L, when V not= L?

jul 10 at 3:32 Joel David Hamkins 74.9k●7●187●343

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Concerning the various proofs from the axiom of choice that R^3 admits of surprising geometrical decompositions into circles, skew lines and so on: can we prove in any instance that there are no Borel such decompositions? Or that AC is required?

apr 9 12 at 22:48 Joel David Hamkins 74.9k●7●187●343

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Can there be an almost-special not-fully-special Aronszajn tree?

mar 26 12 at 7:36 Joel David Hamkins 74.9k●7●187●343

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What is the computational-complexity-theoretic analogue of computable inseparability? For example, if P is not NP, are there disjoint NP sets with no separation in P?

mar 1 12 at 14:21 Emil Jeřábek 10.6k●1●24●41

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Does every feasible partial order relation on the natural numbers extend to a feasible linear order relation?

mar 1 12 at 22:06 Jirka Hanika 156●6

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Is every sigma-algebra the Borel algebra of a topology?

feb 9 12 at 8:38 Jochen Wengenroth 1,534●1●13

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Can we find strong fixed-points in the fixed-point lemma of Gödel’s incompleteness theorem, that is, where the fixed point is syntactically identical to its substitution instance rather than merely provably equivalent to it?

apr 11 12 at 2:12 Ali Enayat 4,459●1●9●23

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What is the spectrum of possible cofinality types for cuts in an ordered field? Or in a model of the hyperreals? Or in a nonstandard model of arithmetic?

aug 12 11 at 10:36 Emil Jeřábek 10.6k●1●24●41

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