Article in volume
Authors:
Sorasak Leeratanavalee
Research Group in Mathematics and Applied Mathematics
Department of Mathematics, Faculty of Science
Chiang Mai University
Chiang Mai 50200, Thailand
email: sorasak.l@cmu.ac.th
Title:
The partial many-sorted algebras of terms and formulas with fixed variables count
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 339-362
Received: 2022-02-03 , Revised: 2022-04-20 , Accepted: 2022-04-20 , Available online: 2023-10-06 , https://doi.org/10.7151/dmgaa.1444
Abstract:
Terms and formulas, which are formal expressions in first and second order
languages obtained by alphabets, operation symbols, and relation symbols, are
used to study algebras and algebraic systems. In this paper, we introduce the
notion of terms with fixed variables count. The partial many-sorted
superposition operations of such terms and their partial many-sorted algebra
satisfying clone axioms as weak identities are presented. We also extend our
structures from algebras to algebraic systems via the concept of formulas
with fixed variables count. Conditions for the set of such formulas to
be closed under taking of superposition of formulas are determined. We construct
the partial many-sorted algebra of formulas with fixed variables count and
investigate its satisfaction by clone axioms. Finally, we prove that such
partial structure is isomorphic to some Menger systems of the same rank of
partial multiplace functions.
Keywords:
partial many-sorted algebra, term, formula, partial operation, representation
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