Cylindric Set Algebras

Henkin, Leon; Monk, J. Donald; Tarski, Alfred; Andréka, Hajnal; Németi, István

doi:10.1007/bfb0095612

Cited by 74 publications

(72 citation statements)

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“…first order axiomatizable) class. In [17,II.8.6,p. 266], Andréka and Németi provide a negative answer for the cylindric case but only for the lowest value of α.…”

Section: History (Previous Results)mentioning

confidence: 99%

The class of 2-dimensional neat reducts is not elementary

Ahmed

2002

Fund. Math.

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[29], neat reducts are studied in connection to (isomorphism types of) algebras of sentences of first order logic. In [27] a N ET is formulated and proved which implies the completeness of certain finitary fragments of Keisler's logics that are also expansions of first order logic without equality. This provides a solution to the so-called finitization problem in Algebraic Logic. In fact, the N ET has proved to be a successful strategy to address different versions of the finitization problem (see e.g. [35]). Very 2000 Mathematics Subject Classification: Primary 03G15; Secondary 06E25, 08B99.

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“…first order axiomatizable) class. In [17,II.8.6,p. 266], Andréka and Németi provide a negative answer for the cylindric case but only for the lowest value of α.…”

Section: History (Previous Results)mentioning

confidence: 99%

The class of 2-dimensional neat reducts is not elementary

Ahmed

2002

Fund. Math.

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“…For a survey of the theory of these algebras the reader is referred to Chapter 5 of [Henkin, Monk & Tarski 1985]; here we confine ourselves to the definitions and those facts that we need later on. Let α be an arbitrary but fixed ordinal.…”

Section: Diagonal-free Cylindric Algebrasmentioning

confidence: 99%

Undecidable theories of Lyndon algebras

Stebletsova¹,

Venema²

2001

J. symb. log.

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With each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski's axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class L(G) of Lyndon algebras associated with projective geometries in G has an undecidable equational theory. In our proof we develop and use a connection between projective geometries and diagonal-free cylindric algebras.

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“…[7, The definitions of RA and CAa, both originating with Tarski, can be found e.g. in [5,7,8,10] and in [5,6] respectively. Below we recall that part of their definitions that will be needed in the present paper.…”

Section: Boolean Reducts Of Relation and Cylindric Algebras And The Cmentioning

confidence: 99%