3 citations · 9 across the 57 of their papers we have counts for
59 papers
Space and time via Topological and Tense cylindric algebras
Tarek Sayed Ahmed
Let be an arbritary ordinal, and . In \cite{3} accepted for publication in Quaestiones Mathematicae, we studied using algebraic logic, interpolation, amalgamation using…
An infinite stratum of representability; some cylindric algebras are more representable than others
Tarek Sayed Ahmed
Let . Let $\CA_n$ denote the class of cylindric algebras of dimension and $\RCA_n$ denote the class of representable $\CA_n$s. We say that $\A\in \RCA_n$ is repres…
Completely representable neat reducts
Tarek Sayed Ahmed
For an ordinal , denotes the class of polyadic equality algebras of dimension . We show that for several classes of algebras that are reducts of $\PEA_ω$ whose si…
Non elementary classes of relation and cylindric algebras
Tarek Sayed Ahmed
For any pair of ordinals , denotes the class of cylindric algebras of dimension , denote the class of representable s and ($…
A universal approach to Omitting types for various multimodal and quantifier logics
Tarek Sayed Ahmed
We intend to investigate the metalogical property of 'omitting types' for a wide variety of quantifier logics (that can also be seen as multimodal logics upon identifying existenti…
Hilbert's tenth problem, Gödel's incompleteness, Halting problem, a unifying perspective
Tarek Sayed Ahmed
We formulate a property on a class of relations on the natural numbers, and formulate a general theorem on , from which we get as corollaries the insolvability of Hilbert's…
Atom-canonicity in algebraic logic in connection to omitting types in modal fragments of L_{ω, ω}
Tarek Sayed Ahmed
Fix 2<n<ω. Let L_n denote first order logic restricted to the first n variables. CA_n denotes the class of cylindric algebras of dimension n and for m>n, Nr_n\CA_m(\subseteq CA_n)…
A brief history of algebraic logic from neat embeddings to rainbow constructions
Tarek Sayed Ahmed
We take a long magical tour in algebraic logic, starting from classical results on neat embeddings due to Henkin, Monk and Tarski, all the way to recent results in algebraic logic…
Finite relation algebras and omitting types in modal fragments of first order logic
Tarek Sayed Ahmed
Let 2<n\leq l<m< ω. Let L_n denote first order logic restricted to the first n variables. We show that the omitting types theorem fails dramatically for the n--variable fragments o…
Splitting methods in algebraic logic: Proving results on non-atom-canonicity, non-finite axiomatizability and non-first oder definability for cylindric and relation algebras
Tarek Sayed Ahmed
We deal with various splitting methods in algebraic logic. The word `splitting' refers to splitting some of the atoms in a given relation or cylindric algebra each into one or more…
A solution to the finitizability problem for quantifier logics with equality
Tarek Sayed Ahmed
We consider countable so-called rich subsemigroups of (ωω,\circ); each such semigroup gives a variety CPEA_T that is axiomatizable by a finite schema of equations taken in a co…
Problems on neat embeddings solved by rainbow constructions and Monk algebras
Tarek Sayed Ahmed
This paper is a survey of recent results and methods in (Tarskian) algebraic logic. We focus on cylindric algebras. Fix 2<n<ω. Rainbow constructions are used to solve problems on c…
Atom-canonicity and complete representations for cylindric-like algebras, and omitting types for the clque guarded fragment of first order logic
Tarek Sayed Ahmed
Fix a finite ordinal n>2. We show that there exists an atomic, simple and countable representable CA_n, such that its minimal completion is outside SNr_nCA_{n+3}. Hence, for any fi…
Algebraic analysis of temporal and topological finite variable fragments, using cylindric modal algebras
Tarek Sayed Ahmed
We study what we call topological cylindric algebras and tense cylindric algebras defined for every ordinal . The former are cylindric algebras of dimension expanded with $\…
Amalgamation, interpolation and congruence extension properties in topological cylindric algebras
Tarek Sayed Ahmed
Topological cylindric algebras of dimension α, αany ordinal are cylindric algebras with dimension αexpanded with αS4 modalities. The S4 modalities in representable algebras are ind…
Algebraisable versions of predicate topological logic
Tarek Sayed Ahmed
Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric rel…
Dedekind completions, neat embeddings and omitting types
Tarek Sayed Ahmed
Let n be finite >2. We show that any class between S\Nr_n\CA_{n+3} and RCA_n is not atom canonical, and any class containing the class of completely representable algebras and cont…
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…