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The free will theorem states: Given the axioms, if the choice about what measurement to take is not a function of the information accessible to the experimenters (free will assumption), then the results of the measurements cannot be determined by anything previous to the experiments. That is an "outcome open" theorem:
By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled. A hidden variables theory which is superdeterministic can thus fulfill Bell's notion of local causality and still violate the inequalities derived from Bell's theorem. [1]
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In the mathematical field of set theory, Martin's axiom, introduced by Donald A. Martin and Robert M. Solovay, [1] is a statement that is independent of the usual axioms of ZFC set theory. It is implied by the continuum hypothesis , but it is consistent with ZFC and the negation of the continuum hypothesis.
Similarly, if A is a closed set, then the game is determined. By the Borel determinacy theorem, games whose winning set is a Borel set are determined. It follows from the existence of sufficiently large cardinals that AD holds in L(R) and that a game is determined if it has a projective set as its winning set (see Projective determinacy).
Semantic completeness is the converse of soundness for formal systems. A formal system is complete with respect to tautologousness or "semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically valid formulas: formulas that are true under every interpretation of the language of the system ...
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Chicken Soup for the Soul Studios has picked up two new shows, including a new wedding talk show hosted by Olympic figure skater Tara Lipinski, and renewed Joe Morton’s Crackle series “Inside ...