Heyting $$\kappa $$ -框架

Pub Date : 2023-10-07 DOI:10.1007/s11225-023-10072-3

Hector Freytes, Giuseppe Sergioli

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引用次数: 0

摘要

摘要在具有无穷运算的代数框架下，研究了$$\bigvee _{\kappa }$$ κ -完备Heyting代数或Heyting $$\kappa $$ κ -框架的方程理论。给出了一个可代数的希尔伯特式微积分。基于Heyting $$\kappa $$ κ -frames的无穷结构，也得到了一个与frames的$$\langle \bigvee , \wedge , \rightarrow , 0 \rangle $$⟨，∧，→，0⟩-结构相关的等式型完备定理。

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Heyting $$\kappa $$-Frames

Abstract In the framework of algebras with infinitary operations, the equational theory of $$\bigvee _{\kappa }$$ ⋁ κ -complete Heyting algebras or Heyting $$\kappa $$ κ -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting $$\kappa $$ κ -frames, an equational type completeness theorem related to the $$\langle \bigvee , \wedge , \rightarrow , 0 \rangle $$ ⟨ ⋁ , ∧ , → , 0 ⟩ -structure of frames is also obtained.

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