Heyting $$\kappa $$ -框架

IF 0.6 3区数学 Q2 LOGIC

Studia Logica 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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来源期刊

Studia Logica MATHEMATICS-LOGIC

CiteScore

1.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The leading idea of Lvov-Warsaw School of Logic, Philosophy and Mathematics was to investigate philosophical problems by means of rigorous methods of mathematics. Evidence of the great success the School experienced is the fact that it has become generally recognized as Polish Style Logic. Today Polish Style Logic is no longer exclusively a Polish speciality. It is represented by numerous logicians, mathematicians and philosophers from research centers all over the world.