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Algebra |
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Authors: Shao-Dan Lee
Suppose that L is a first-order language. Let Lu2020 denote the union of L and {t, f} where t(true), f(false) are the nullary operations. We may define a binary relation ‘≤’ such that the sentences set Φ of the language Lu2020 is a preordered set. And we may construct a boolean algebra Φ/∼, denoted Φ ̃ , by an equivalence relation ‘∼’. Then Φ ̃ is a partial ordered set. Let A be a structure of the language L. If Th(A) is a theory of A, then Thu2020(A) is an ultrafilter. If Ψ ⊂ Φ ̃ is a finitely generated filter, then Ψ is principal. We may define a kernel of a homomorphism of the boolean algebra Φ ̃ such that the kernel is a filter. And a filter is a kernel if it is satisfied by some assumptions.
Comments: 9 Pages.
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[v1] 2023-03-14 03:19:03
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