The class of 2-dimensional neat reducts is not elementary

• Autorzy: Tarek Sayed Ahmed
• Języki publikacji: EN

Abstrakty

EN

SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends to higher dimensions is open.

Kategorie tematyczne

• 06E25: Boolean algebras with additional operations (diagonalizable algebras, etc.)
• 08B99: None of the above, but in this section
• 03G15: Cylindric and polyadic algebras; relation algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 172
• Numer: 1
• Strony: 61-81

Daty

wydano

2002

Twórcy

autor

Tarek Sayed Ahmed

• Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

Identyfikatory

DOI

10.4064/fm172-1-5