27,075 research outputs found
Generic absoluteness and boolean names for elements of a Polish space
It is common knowledge in the set theory community that there exists a
duality relating the commutative -algebras with the family of -names
for complex numbers in a boolean valued model for set theory . Several
aspects of this correlation have been considered in works of the late 's
and early 's, for example by Takeuti, and by Jech. Generalizing Jech's
results, we extend this duality so as to be able to describe the family of
boolean names for elements of any given Polish space (such as the complex
numbers) in a boolean valued model for set theory as a space
consisting of functions whose domain is the Stone space of , and
whose range is contained in modulo a meager set. We also outline how this
duality can be combined with generic absoluteness results in order to analyze,
by means of forcing arguments, the theory of .Comment: 27 page
Compactly generating all satisfying truth assignments of a Horn formula
As instance of an overarching principle of exclusion an algorithm is
presented that compactly (thus not one by one) generates all models of a Horn
formula. The principle of exclusion can be adapted to generate only the models
of weight . We compare and contrast it with constraint programming,
integer programming, and binary decision diagrams.Comment: Considerably improves upon the readibility of the previous versio
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