HH∗−intuitionistic heyting valued Ω-algebra and homomorphism

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Mersin, iftlikky Campus, Mersin, Turke

2 Department of Mathematics, University of Mersin, iftlikky Campus, Mersin, turke

Abstract

Intuitionistic Logic was introduced by L. E. J. Brouwer in[1] and Heyting algebra was defined by A. Heyting to formalize the Brouwer’s intuitionistic logic[4]. The concept of Heyting algebra has been accepted as the basis for intuitionistic propositional logic. Heyting algebras have had applications in different areas. The coHeyting algebra is the same lattice with dual operation of Heyting algebra[5]. Also, co-Heyting algebras have several applications in different areas. In this paper, we introduced the new concept HH∗− Intuitionistic Heyting Valued Ω-Algebra. The purpose of introducing this new concept is to expand the field of researchers’ area using both membership degree and non-membership degree. This allows us to get more sensitive results.The HH∗− Intuitionistic Heyting valued set, HH∗− Intuitionistic Heyting valued relation, HH∗− Intuitionistic Heyting valued Ω-algebra and the homomorphism over HH∗− Intuitionistic Heyting valued Ω-algebra were defined.

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References

[1] Brouwer, L. E. J., Intuitionism and Formalism, English translation by A. Dres-den, Bulletin of the American Mathematical Society, 20 (1913): 81–96,reprinted in Benacerraf and Putnam(eds.)1983:77–89;also reprinted in Heyting (ed.)1975: 123–138.
[2] C¸ uvalcı˘glu G., Heyting Valued Omega Free Algebra, C¸ ukurova University Institute of Science and Technology, PhD Thesis, Adana, 2002, 68 p.
[3] Faith C., Algebra: Rings, Modules and Categories I, Springer-Verlag, Berlin
[4] Heyting, A. “Die formalen Regeln der intuitionistischen Logik,” in three parts, Sitzungsberichte der preussischen Akademie der Wissenschaften: 42–71, 158–169,1930. English translation of Part I in Mancosu 1998: 311–327.
[5] Lawvere F.V. , Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes, in A.Carboni, et.al., Category theory, Proccedings, Como. 1990. 
Journal of Hyperstructures
Volume 6, Spec. 13th AHA
July 2017
Pages 72-82

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