3 citations · 9 across the 57 of their papers we have counts for
42 papers · 1 filter
Cylindric and polyadic algebras, new perspectives
Tarek Sayed Ahmed
We generalize the notion of Monk's schema in such a way to integrate finite dimensions. This allows us to lift a plathora of deep results proved for finite dimensions to the infini…
Atom-canonicity, relativized representations and omitting types for clique guarded semantics and guarded logics
Tarek Sayed Ahmed
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativiz…
Strongly representable atom structures and neat embeddings
Tarek Sayed Ahmed, Mohammed Khaled
In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not element…
On completions, neat embeddings and omittings types, yet again
Tarek Sayed Ahmed
In this paper we investigate using the methodology of algebraic logic, deep algebraic results to prove three new omitting types theorems for finite variable fragments of first orde…
A polyadic algebra of infinite dimension is completely representable if and only if it is atomic and completely additive
Tarek Sayed Ahmed
We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infi…
For finite n\geq 3, and k\geq 4, the variety SNr_n\CA_{n+k} is not atom canonical
Tarek Sayed Ahmed
We show that there exists an atomic representable polyadic equality algebra of finite dimension n\geq 3, such that the cylindric reduct of its completion is not in SNr_n\CA_{n+4},…
There is no finite variable axiomatization for various diagonal free algebras
Tarek Sayed Ahmed
We show, using a ranbow construction for cylindric algebras, that for any class K between diagonal free cylindric algebras and polyadic equality algebras of finite dimension > 2, t…
Blowing up and blurring finite Monk and rainbow algebras
Tarek Sayed Ahmed
We use Monk like algebras to give a new proof that the classes of strongly representable relation algebras and finite dimensional cylindric algebras of dimension >2 are not element…
Various interplays between relation and cylindric algebras
Tarek Sayed Ahmed
Using model theoretic techniques that proved that the class of neat reducts of dimensional cylindric algebras, $\Nr_n\CA_m$, is not elementary, we prove the same result for…
Strongly representable algebras
Tarek Sayed Ahmed
We give a simpler proof of a result of Hodkinson in the context of a blow and blur up construction argueing that the idea at heart is similar to that adopted by Andréka et all \cit…
On neat atom structures for cylindric like algebras
Tarek Sayed Ahmed
(1) Let 1\leq k\leq ω. Call an atom structure αweakly k neat representable, the term algebra is in \RCA_n\cap \Nr_n\CA_{n+k}, but the complex algebra is not representable. Call an…
On atomicity of free algebras in Boolean algebras with operators, and a new result on Pinter's free algebras
Tarek Sayed Ahmed
We give some general theorems on free algebras of varieties of Boolean algebras with operators; a hitherto new result is obtained for Pinter's substitution algebras. For n\geq 3, a…
Strongly representable atom structures
Tarek Sayed Ahmed, Mohamed Khalifa
Using constructions of Hirsch and Hodkinson, we show that the class of strongly atom structures for various cylindric-like algebras is not elementary. This applies to diagonal free…
Blow up and Blur constructions in Algebraic Logic
Tarek Sayed Ahmed
The idea in the title is to blow up a finite structure, replacing each 'colour or atom' by infinitely many, using blurs to represent the resulting term algebra, but the blurs are n…
On completions of algebras in SNr_nCA_{n+k}, n\geq 3, k\geq 1
Tarek Sayed Ahmed
We give a sufficient condition that implies that SNr_nCA_{n+k}, n\geq 3, k\geq 3 (both finite)is not closed under completions. We compare this condition to existing results in lite…
Results on Polyadic Algebras
Tarek Sayed Ahmed
While every polyadic algebra ($\PA$) of dimension 2 is representable, we show that not every atomic polyadic algebra of dimension two is completely representable; though the class…
Logics to which the class of neat reducts is sensitive to
Tarek Sayed Ahmed
Let L be a quantifier predicate logic. Let K be a class of algebras. We say that K is sensitive to L, if there is an algebra in K, that is L interpretable into an another algebra,…
The elementary closure of the class Nr_nCA_m for m\geq n+1 is not finitely axiomatizable, futhermore for any finite k\geq 1, there is A\in Nr_ωCA_{\omeg+k}that is not SNr_ωCA_{ω+k+1}
Tarek Sayed Ahmed
We show that for 1<n<m, the class Nr_nCA_m known to be non-elementary is pseudo elementary. When n and m are finite we use a two sorted theory, when n is finite and m infinite we u…
Completeness and interpolation for intuitionistic infinitary predicate logic, in connection to finitizing the class of representable Heyting polyadic algebras
Tarek Sayed Ahmed
We study different representation theorems for various reducts of Heyting polyadic algebras. Superamalgamation is proved for several (natural reducts) and our results are compared…
Amalgmation in Boolean algebras with operators
Tarek Sayed Ahmed
We study various forms of amalgamation for Boolean algebras with operations. We will also have the occasion to weaken the Boolean structure dealing with MV and BL algebras with ope…
On finitely generated reducts of polyadic equality algebras
Tarek Sayed Ahmed
Extending a deep result of Andreka and Nemeti, we show that unlike the dimension complemented case, there are weak set quasi-polyadic simple algebras of dimension >1, that are fini…
Polyadic-like algebras without the amalgamation property
Tarek Sayed Ahmed
Usually when we have polyadic-like algebras, meaning that we have infinitary substitutions (that is substitutions moving infinitely many points) in the similarity type, then we get…
Building relativized representations using games
Tarek Sayed Ahmed, Mohamed Khaled
We prove the celebrated representation theorem of Andreka-Resek-Thompson, together with its polyadic analogue by Ferenczi, using games as introduced in algebraic logic by Hirsch an…
Some metalogical properties for infinitary predicate topological logic
Tarek Sayed Ahmed
We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topolog…