Krull dimension of commutative ring is helpful to some concepts, i.e. <dimension by cut and glue>, <string and i-string>, <world and anti-world> and <true and false>.
Outline for reconstruction is roughly expressed by the next.
(1) Element of meaning on word is expressed by prime ideal.
(2) Word has dimension that is expressed by height of prime ideal’s maximum value.
(3) Word is expressed by Noetherian ring or Artinian ring.
(4) Sentence is expressed by exact sequence that contains direction of sentence which is expressed by covariant functor and Contravariant functor.
(5) Concept of string and i-string on sentence is connected with true and false in comparison with localization of commutative ring that contains algebraic set, Spec (A) and Zariski topology.
(6) Zariski topology satisfies axiomatic system of closed set.
(7) Axiom of choice is considered from the root of the theory for word and sentence.
[References]
[Reference premise]
Tokyo September 26, 2007
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