{"title":"Heyting $$\\kappa $$-Frames","authors":"Hector Freytes, Giuseppe Sergioli","doi":"10.1007/s11225-023-10072-3","DOIUrl":null,"url":null,"abstract":"Abstract In the framework of algebras with infinitary operations, the equational theory of $$\\bigvee _{\\kappa }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mo>⋁</mml:mo> <mml:mi>κ</mml:mi> </mml:msub> </mml:math> -complete Heyting algebras or Heyting $$\\kappa $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>κ</mml:mi> </mml:math> -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting $$\\kappa $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>κ</mml:mi> </mml:math> -frames, an equational type completeness theorem related to the $$\\langle \\bigvee , \\wedge , \\rightarrow , 0 \\rangle $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:mo>⋁</mml:mo> <mml:mo>,</mml:mo> <mml:mo>∧</mml:mo> <mml:mo>,</mml:mo> <mml:mo>→</mml:mo> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> -structure of frames is also obtained.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"108 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Logica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11225-023-10072-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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