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Tarek Sayed Ahmed

Publications and source records attributed to Tarek Sayed Ahmed.

60 records · Page 4Linked to original sources
arXiv2013

Neat atom structures

An atom structure is neat if there an algebra based on this atom structure in Nr_nCA_ω. We show that this class is not elementary

math.LO↗
arXiv2013

What is the spirit of the cylindric paradigm, as opposed to that of the polyadic one?

We give a categorial definition separating cylindric-like algebras from polyadic-like ones. Viewing the neat reduct operator as a functor, we show that it does not have a right adjoint in the former case, but it is strongly invertible in the second case. Several new results on amalgamation, and non finite axiomatizability are presented for both paradigms. A hitherto categorial equivalence is also given between relation algebras with quasi-projections and Nemeti's directed cylindric algebras for any dimension.

math.LO↗
arXiv2013

On the multi dimensional modal logic of substitutions

We prove completeness, interpolation, decidability and an omitting types theorem for certain multi dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing (varieties generated by) complex algebras of Kripke semantics for such logic. Those algebras, whose elements are sets of states are common reducts of cylindric and polyadic algebras

math.LO↗
arXiv2013

On the finitizability problem in algebraic logic; recent results

This is a survey article in algebraic logic, where we take a magical tour from old concepts due to Henkin, Monk and Tarski like neat embeddings, to modern views and perspectives, culminating in the use of Erdos graphs in settling important questions in algebraic logic.

math.LO↗