A Neat Embedding Theorem for Expansions of Cylindric Algebras

Sayed-Ahmed, Tarek; Samir, Basim

doi:10.1093/jigpal/jzl032

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Introduction2

Wwwmlq-journalorg1

Omitting Types For Finite Variable Fragments1

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2008

2022

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Cited by 9 publications

(4 citation statements)

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“…In other words, we can dispense with some of the CA axioms when we get to ω extra dimensions. We note that FPEA α enjoys a NET as well [15]. It is known that for infinite α, Dc α ⊆ Nr α CA β for all β > α [7, Theorem 2.6.74].…”

Section: Wwwmlq-journalorgmentioning

confidence: 94%

A note on substitutions in representable cylindric algebras

Ahmed¹

2009

Mathematical Logic Qtrly

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Section: Wwwmlq-journalorgmentioning

confidence: 94%

A note on substitutions in representable cylindric algebras

Ahmed¹

2009

Mathematical Logic Qtrly

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“…We note that our construction quite easily leads to the (new) fact that the Omitting Types Theorem fails for finite first order definable extensions of finite variable fragments of first order logic studied in [5] and [16] as long as the number of variables is > 2.…”

Section: Omitting Types For Finite Variable Fragmentsmentioning

confidence: 97%

Weakly representable atom structures that are not strongly representable, with an application to first order logic

Ahmed¹

2008

Mathematical Logic Qtrly

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Let n > 2. A weakly representable relation algebra that is not strongly representable is constructed. It is proved that the set of all n by n basic matrices forms a cylindric basis that is also a weakly but not a strongly representable atom structure. This gives an example of a binary generated atomic representable cylindric algebra with no complete representation. An application to first order logic is given.

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“…This is not the end of the story; in fact, this is where the fun begins. A new unexpected viewpoint can yield dividends, and indeed the notion of neat reducts has been revived lately, to mention a few references: [3], [4], [2], [5], [1], [31], [53], [20], [23], [19], and [7]. In this paper, we survey (briefly) such results on neat reducts, putting them in a wider perspective.…”

Section: Introductionmentioning

confidence: 99%