On atomicity of free algebras in certain cylindric-like varieties

Gyenis, Zalán

doi:10.1093/jigpal/jzp098

Cited by 11 publications

(11 citation statements)

References 5 publications

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“…Atoms in these free algebras correspond to finitely axiomatizable complete and consistent theories, while the atomicity of these free algebras correspond to the failure of Gödel's incompleteness theorem for the corresponding logics. For more details about this correspondence, see [10], [42], [43], [33] and [35].…”

Section: Introductionmentioning

confidence: 99%

First order logic without equality on relativized semantics

Banerjee

Khaled

2018

Annals of Pure and Applied Logic

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Let α ≥ 2 be any ordinal. We consider the class Drsα of relativized diagonal free set algebras of dimension α. With same technique, we prove several important results concerning this class. Among these results, we prove that almost all free algebras of Drsα are atomless, and none of these free algebras contains zero-dimensional elements other than zero and top element. The class Drsα corresponds to first order logic, without equality symbol, with α-many variables and on relativized semantics. Hence, in this variation of first order logic, there is no finitely axiomatizable, complete and consistent theory.2010 Mathematics Subject Classification. Primary 03G15, 03B45, 03C95. Secondary 03G25, 03C05, 08B20.

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Section: Introductionmentioning

confidence: 99%

First order logic without equality on relativized semantics

Banerjee

Khaled

2018

Annals of Pure and Applied Logic

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Section: Introductionmentioning

confidence: 99%

“…These properties were defined by I. Németi in 1985 and named by him in appreciation of the pioneering work of K. Gödel. For more details concerning these incompleteness properties, see [4,14,17,15,18].Normal forms are essentially used in establishing results in both algebra and logic, e.g.[10], [12] and [13]. In the application section, we apply our general theorem to produce normal forms for Boolean algebras with operators.…”

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confidence: 99%

General normal forms for any additive logic

Khaled

2017

Studia Scientiarum Mathematicarum Hungarica

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In this article, we define general normal forms for any logic that has propositional part and whose non-propositional connectives distribute over the finite disjunctions. We do not require the non-propositional connectives to be closed on the set of formulas, so our normal forms cover logics with partial connectives too. We also show that most of the known normal forms in the literature are in fact particular cases of our general forms. These general normal forms are natural improvement of the distributive normal forms of J. Hintikka [2] and their modal analogues, e.g. [1] and [3].

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“…The non-atomicity of the free algebras of logics is equivalent to weak Gödel's incompleteness property of the corresponding logic. See (Németi, 1985, proposition 8) and (Gyenis, 2011).…”

Section: Introductionmentioning

confidence: 99%

Weak Godel's incompleteness property for some decidable versions of the calculus of relations

Khaled

2015

Preprint

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Relativization is one of the central topics in the study of algebras of relations. Some relativized relation algebras behave much nicer than the original relation algebras. In this paper, we study the atomicity of the finitely generated free algebras of these nice classes of relativized relation algebras. In particular, we give an answer for the open problem, posed by I. Németi in 1985, which asks whether the finitely generated free algebras of the class of the weak associative relation algebras W A are atomic or not.

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On atomicity of free algebras in certain cylindric-like varieties

Cited by 11 publications

References 5 publications

First order logic without equality on relativized semantics

First order logic without equality on relativized semantics

General normal forms for any additive logic

Weak Godel's incompleteness property for some decidable versions of the calculus of relations

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