关于Bellissima关于生成的自由Heyting代数的构造及其他
On Bellissima's construction of the finitely generated free Heyting algebras, and beyond
摘要：
本文从拓扑学和模型论的角度研究了非生成的自由Heyting代数。我们审查Bellissima的代表性的生成的自由海廷代数，我们证明，它产生一个嵌入profinite完成，这也是完成相对于一个自然定义的度量。我们给出了一个代数解释的Kripke模型Bellissima作为主理想sprectrum，并表明它是一阶解释的海廷代数，从几个模型的理论和代数性质的衍生。例如，我们证明了一个自由生成的Heyting代数只有一组自由生成元，这组自由生成元是可定义的，从而它的自同构群是它的生成元上的置换群.
英文摘要：
We study finitely generated free Heyting algebras from a topological and from a model theoretic point of view. We review Bellissima's representation of the finitely generated free Heyting algebra; we prove that it yields an embedding in the profinite completion, which is also the completion with respect to a naturally defined metric. We give an algebraic interpretation of the Kripke model used by Bellissima as the principal ideal sprectrum and show it to be first order interpretable in the Heyting algebra, from which several model theoretic and algebraic properties are derived. For example we prove that a free finitely generated Heyting algebra has only one set of free generators, which is definable in it. As a consequence its automorphism group is the permutation group over its generators.
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