Tarek Sayed-Ahmed - Academia.edu (original) (raw)

Papers by Tarek Sayed-Ahmed

Research paper thumbnail of Neat embeddings as adjoint situations

Synthese, Sep 26, 2013

Looking at the operation of forming neat α-reducts as a functor, with α an infinite ordinal, we i... more Looking at the operation of forming neat α-reducts as a functor, with α an infinite ordinal, we investigate when such a functor obtained by truncating ω dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorical result to several amalgamation properties for classes of representable algebras. 1

Research paper thumbnail of The number of countable models via Algebraic logic

Vaught's Conjecture states that if T is a complete first order theory in a countable language tha... more Vaught's Conjecture states that if T is a complete first order theory in a countable language that has more than ℵ 0 pairwise non isomorphic countable models, then T has 2 ℵ 0 such models. Morley showed that if T has more than ℵ 1 pairwise non isomorphic countable models, then it has 2 ℵ 0 such models. In this paper, we first show how we can use algebraic logic, namely the representation theory of cylindric and quasi-polyadic algebras, to study Vaught's conjecture (count models), and we reprove Morley's above mentioned theorem. Second, we show that Morley's theorem holds for the number of non isomorphic countable models omitting a countable family of types. We go further by giving examples showing that although this number can only take the values given by Morley's theorem, it can be different from the number of all non isomorphic countable models. Moreover, our examples show that the number of countable models omitting a family of types can also be either ℵ 1 or 2 and therefore different from the possible values provided by Vaught's conjecture and by his well known theorem; in the case of ℵ 1 , however, the family is uncountable. Finally, we discuss an omitting types theorem of Shelah. The algebraic proof of Morley's theorem has been independently examined, essentially the same way, by T.S. Ahmed and M. Assem in Cairo and by G. Sági and D. Sziráki in Budapest, (see [12]). The rest of the paper is the joint work of the authors.

Research paper thumbnail of An Interpolation Theorem for First Order Logic with Infinitary Predicates

Logic Journal of the IGPL, Aug 16, 2006

Expressions in formal systems are written in primitive notation. However, the fact that first ord... more Expressions in formal systems are written in primitive notation. However, the fact that first order logic may be identified with natural numbers (via Godel numbering) and hence with finite sets makes it no longer necessary to regard formulas as finite primitive inscriptions. This ...

Research paper thumbnail of Independence Results in Algebraic Logic

Logic Journal of IGPL, 2006

Abstract We formulate several statements in Algebraic Logic that turn out to be independent of ZF... more Abstract We formulate several statements in Algebraic Logic that turn out to be independent of ZFC. We relate such statements to Martin's axiom, omitting types for variants of first order logic and topological properties of Baire spaces.

Research paper thumbnail of Amalgamation Theorems in Algebraic Logic, an overview

Logic Journal of IGPL, 2005

We review, and in the process unify two techniques (due to Németi and Pigozzi), for proving resul... more We review, and in the process unify two techniques (due to Németi and Pigozzi), for proving results con-cerning amalgamation in several classes studied in algebraic logic. The logical counterpart of these results adress interpolation and definability properties in modal and algebraic ...

Research paper thumbnail of The class of neat reducts is not elementary

Logic Journal of IGPL, 2001

... by Tarek Sayed Ahmed. Add To MetaCart. ...

Research paper thumbnail of SVC and AC load voltage regulation scheme for DC outputted three-phase induction generator

Power Electronics and …, 2004

In this paper, the terminal voltage of the three-phase self-excited induction generator (SEIG) dr... more In this paper, the terminal voltage of the three-phase self-excited induction generator (SEIG) driven by a variable-speed prime mover (VSPM) is maintained constant by using static VAr compensator (SVC) and the AC load voltage regulator (AC-LVR) for DC ...

Research paper thumbnail of The Class Snr (3) CA (k) is Not Closed Under Completions (vol 16, pg 427, 2008)

We show that SNr_nCA_m is not atom canoical for all 2<m<\omega, and m\geq n)n1)/2+1.

Research paper thumbnail of ZVS-PWM Boost Chopper-Fed DC-DC Converter with Load-Side Auxiliary Edge Resonant Snubber and Its Performance Evaluations

Journal of Power Electronics, 2004

Research paper thumbnail of A non representable infinite dimensional quasi-polyadic equality algebra with a representable cylindric reduct

Studia Scientiarum Mathematicarum Hungarica, 2013

We construct an infinite dimensional quasi-polyadic equality algebra \documentclass{aastex} \usep... more We construct an infinite dimensional quasi-polyadic equality algebra \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} mathfrakA\mathfrak{A}mathfrakA \end{document} such that its cylindric reduct is representable, while \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} mathfrakA\mathfrak{A}mathfrakA \end{document} itself is not representable.

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

MLQ, 2008

Let n > 2. A weakly representable relation algebra that is not strongly representable is construc... more 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.

Research paper thumbnail of Classes of algebras without the amalgamation property

Logic Journal of IGPL, 2010

ABSTRACT A table in [J. Madárasz and T. Sayed-Ahmed, “Amalgamation, interpolation and epimorphism... more ABSTRACT A table in [J. Madárasz and T. Sayed-Ahmed, “Amalgamation, interpolation and epimorphisms in algebraic logic”, Algebra Univers. 56, No. 2, 179–210 (2007; Zbl 1122.03063)] listed whether or not seven classes of infinite-dimensional cylindric algebras have ten variations on the amalgamation property, but left nine open problems, which are all solved in this paper.

Research paper thumbnail of A pr 2 01 3 Interpolation in many valued logics using algebraic logic

We prove several interpolation theorems for many valued infinitary logic with quantifiers, by stu... more We prove several interpolation theorems for many valued infinitary logic with quantifiers, by studying expansions of MV algebras in the spirit of polyadic and cylindric algebras.

Research paper thumbnail of Problems on neat embeddings solved by rainbow constructions and Monk algebras

This paper is a survey of recent results and methods in (Tarskian) algebraic logic. We focus on c... more This paper is a survey of recent results and methods in (Tarskian) algebraic logic. We focus on cylindric algebras. Fix 2<n<\omega. Rainbow constructions are used to solve problems on classes consisting of algebras having a neat embedding property substantially generalizing seminal results of Hodkinson as well as Hirsch and Hodkinson on atom-canonicity and complete representations, respectively. For proving non-atom-canonicity of infinitely many varieties approximating the variety of representable algebras of dimension n, so-called blow up and blur constructions are used. Rainbow constructions are compared to constructions using Monk-like algebras and cases where both constructions work are given. When splitting methods fail. rainbow constructions are used to show that diagonal free varieties of representable diagonal free algebras of finite dimension n, do no admit universal axiomatizations containing only finitely many variables. Notions of representability, like complete, w...

Research paper thumbnail of Axiomatizable

We show that for 2 < n + 1 < m, the class Nr n CA m is psuedo elementary, whose elementary that i... more We show that for 2 < n + 1 < m, the class Nr n CA m is psuedo elementary, whose elementary that is not finitely axiomatizable.

Research paper thumbnail of The class of neat reducts is not Boolean closed

Call a class of algebras K Boolean closed if whenever 𝔄∈K and 𝔅≅𝔄 in some Boolean valued extensio... more Call a class of algebras K Boolean closed if whenever 𝔄∈K and 𝔅≅𝔄 in some Boolean valued extension of the universe of sets, then 𝔅∈K. SC, CA, QA and QEA stand for the classes of Pinter’s substitution algebras Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let 1<n≤ω, n<m and K∈{SC,CA,QA,QEA}. We show that the class 𝔑r n K m of all neat n-reducts of algebra in K m (m-dimensional algebras in K) is not Boolean closed. We also show that 𝔑r n CA m and 𝔑r n SC m regarded as concrete categories are not finitely complete (closed under finite limits).

Research paper thumbnail of A note on cylindric algebras

If two atomic cylindric set algebras of finite dimension >1 are isomorphic, then base-minimali... more If two atomic cylindric set algebras of finite dimension >1 are isomorphic, then base-minimality does not imply that they are lower-base isomorphic. This contrasts the case of Boolean algebras.

Research paper thumbnail of Some metalogical properties for infinitary predicate topological logic

We prove completeness, interpolation and omitting types for certain predicate topological logics ... more 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 topological models of a countable theory

Research paper thumbnail of Axiomatizable

We show that for 2 < n + 1 < m, the class Nr n CA m is psuedo elementary, whose elementary that i... more We show that for 2 < n + 1 < m, the class Nr n CA m is psuedo elementary, whose elementary that is not finitely axiomatizable.

Research paper thumbnail of The class of neat reducts is not Boolean closed

Call a class of algebras K Boolean closed if whenever 𝔄∈K and 𝔅≅𝔄 in some Boolean valued extensio... more Call a class of algebras K Boolean closed if whenever 𝔄∈K and 𝔅≅𝔄 in some Boolean valued extension of the universe of sets, then 𝔅∈K. SC, CA, QA and QEA stand for the classes of Pinter’s substitution algebras Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let 1<n≤ω, n<m and K∈{SC,CA,QA,QEA}. We show that the class 𝔑r n K m of all neat n-reducts of algebra in K m (m-dimensional algebras in K) is not Boolean closed. We also show that 𝔑r n CA m and 𝔑r n SC m regarded as concrete categories are not finitely complete (closed under finite limits).

Research paper thumbnail of Neat embeddings as adjoint situations

Synthese, Sep 26, 2013

Looking at the operation of forming neat α-reducts as a functor, with α an infinite ordinal, we i... more Looking at the operation of forming neat α-reducts as a functor, with α an infinite ordinal, we investigate when such a functor obtained by truncating ω dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorical result to several amalgamation properties for classes of representable algebras. 1

Research paper thumbnail of The number of countable models via Algebraic logic

Vaught's Conjecture states that if T is a complete first order theory in a countable language tha... more Vaught's Conjecture states that if T is a complete first order theory in a countable language that has more than ℵ 0 pairwise non isomorphic countable models, then T has 2 ℵ 0 such models. Morley showed that if T has more than ℵ 1 pairwise non isomorphic countable models, then it has 2 ℵ 0 such models. In this paper, we first show how we can use algebraic logic, namely the representation theory of cylindric and quasi-polyadic algebras, to study Vaught's conjecture (count models), and we reprove Morley's above mentioned theorem. Second, we show that Morley's theorem holds for the number of non isomorphic countable models omitting a countable family of types. We go further by giving examples showing that although this number can only take the values given by Morley's theorem, it can be different from the number of all non isomorphic countable models. Moreover, our examples show that the number of countable models omitting a family of types can also be either ℵ 1 or 2 and therefore different from the possible values provided by Vaught's conjecture and by his well known theorem; in the case of ℵ 1 , however, the family is uncountable. Finally, we discuss an omitting types theorem of Shelah. The algebraic proof of Morley's theorem has been independently examined, essentially the same way, by T.S. Ahmed and M. Assem in Cairo and by G. Sági and D. Sziráki in Budapest, (see [12]). The rest of the paper is the joint work of the authors.

Research paper thumbnail of An Interpolation Theorem for First Order Logic with Infinitary Predicates

Logic Journal of the IGPL, Aug 16, 2006

Expressions in formal systems are written in primitive notation. However, the fact that first ord... more Expressions in formal systems are written in primitive notation. However, the fact that first order logic may be identified with natural numbers (via Godel numbering) and hence with finite sets makes it no longer necessary to regard formulas as finite primitive inscriptions. This ...

Research paper thumbnail of Independence Results in Algebraic Logic

Logic Journal of IGPL, 2006

Abstract We formulate several statements in Algebraic Logic that turn out to be independent of ZF... more Abstract We formulate several statements in Algebraic Logic that turn out to be independent of ZFC. We relate such statements to Martin&amp;#x27;s axiom, omitting types for variants of first order logic and topological properties of Baire spaces.

Research paper thumbnail of Amalgamation Theorems in Algebraic Logic, an overview

Logic Journal of IGPL, 2005

We review, and in the process unify two techniques (due to Németi and Pigozzi), for proving resul... more We review, and in the process unify two techniques (due to Németi and Pigozzi), for proving results con-cerning amalgamation in several classes studied in algebraic logic. The logical counterpart of these results adress interpolation and definability properties in modal and algebraic ...

Research paper thumbnail of The class of neat reducts is not elementary

Logic Journal of IGPL, 2001

... by Tarek Sayed Ahmed. Add To MetaCart. ...

Research paper thumbnail of SVC and AC load voltage regulation scheme for DC outputted three-phase induction generator

Power Electronics and …, 2004

In this paper, the terminal voltage of the three-phase self-excited induction generator (SEIG) dr... more In this paper, the terminal voltage of the three-phase self-excited induction generator (SEIG) driven by a variable-speed prime mover (VSPM) is maintained constant by using static VAr compensator (SVC) and the AC load voltage regulator (AC-LVR) for DC ...

Research paper thumbnail of The Class Snr (3) CA (k) is Not Closed Under Completions (vol 16, pg 427, 2008)

We show that SNr_nCA_m is not atom canoical for all 2<m<\omega, and m\geq n)n1)/2+1.

Research paper thumbnail of ZVS-PWM Boost Chopper-Fed DC-DC Converter with Load-Side Auxiliary Edge Resonant Snubber and Its Performance Evaluations

Journal of Power Electronics, 2004

Research paper thumbnail of A non representable infinite dimensional quasi-polyadic equality algebra with a representable cylindric reduct

Studia Scientiarum Mathematicarum Hungarica, 2013

We construct an infinite dimensional quasi-polyadic equality algebra \documentclass{aastex} \usep... more We construct an infinite dimensional quasi-polyadic equality algebra \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} mathfrakA\mathfrak{A}mathfrakA \end{document} such that its cylindric reduct is representable, while \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} mathfrakA\mathfrak{A}mathfrakA \end{document} itself is not representable.

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

MLQ, 2008

Let n > 2. A weakly representable relation algebra that is not strongly representable is construc... more 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.

Research paper thumbnail of Classes of algebras without the amalgamation property

Logic Journal of IGPL, 2010

ABSTRACT A table in [J. Madárasz and T. Sayed-Ahmed, “Amalgamation, interpolation and epimorphism... more ABSTRACT A table in [J. Madárasz and T. Sayed-Ahmed, “Amalgamation, interpolation and epimorphisms in algebraic logic”, Algebra Univers. 56, No. 2, 179–210 (2007; Zbl 1122.03063)] listed whether or not seven classes of infinite-dimensional cylindric algebras have ten variations on the amalgamation property, but left nine open problems, which are all solved in this paper.

Research paper thumbnail of A pr 2 01 3 Interpolation in many valued logics using algebraic logic

We prove several interpolation theorems for many valued infinitary logic with quantifiers, by stu... more We prove several interpolation theorems for many valued infinitary logic with quantifiers, by studying expansions of MV algebras in the spirit of polyadic and cylindric algebras.

Research paper thumbnail of Problems on neat embeddings solved by rainbow constructions and Monk algebras

This paper is a survey of recent results and methods in (Tarskian) algebraic logic. We focus on c... more This paper is a survey of recent results and methods in (Tarskian) algebraic logic. We focus on cylindric algebras. Fix 2<n<\omega. Rainbow constructions are used to solve problems on classes consisting of algebras having a neat embedding property substantially generalizing seminal results of Hodkinson as well as Hirsch and Hodkinson on atom-canonicity and complete representations, respectively. For proving non-atom-canonicity of infinitely many varieties approximating the variety of representable algebras of dimension n, so-called blow up and blur constructions are used. Rainbow constructions are compared to constructions using Monk-like algebras and cases where both constructions work are given. When splitting methods fail. rainbow constructions are used to show that diagonal free varieties of representable diagonal free algebras of finite dimension n, do no admit universal axiomatizations containing only finitely many variables. Notions of representability, like complete, w...

Research paper thumbnail of Axiomatizable

We show that for 2 < n + 1 < m, the class Nr n CA m is psuedo elementary, whose elementary that i... more We show that for 2 < n + 1 < m, the class Nr n CA m is psuedo elementary, whose elementary that is not finitely axiomatizable.

Research paper thumbnail of The class of neat reducts is not Boolean closed

Call a class of algebras K Boolean closed if whenever 𝔄∈K and 𝔅≅𝔄 in some Boolean valued extensio... more Call a class of algebras K Boolean closed if whenever 𝔄∈K and 𝔅≅𝔄 in some Boolean valued extension of the universe of sets, then 𝔅∈K. SC, CA, QA and QEA stand for the classes of Pinter’s substitution algebras Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let 1<n≤ω, n<m and K∈{SC,CA,QA,QEA}. We show that the class 𝔑r n K m of all neat n-reducts of algebra in K m (m-dimensional algebras in K) is not Boolean closed. We also show that 𝔑r n CA m and 𝔑r n SC m regarded as concrete categories are not finitely complete (closed under finite limits).

Research paper thumbnail of A note on cylindric algebras

If two atomic cylindric set algebras of finite dimension >1 are isomorphic, then base-minimali... more If two atomic cylindric set algebras of finite dimension >1 are isomorphic, then base-minimality does not imply that they are lower-base isomorphic. This contrasts the case of Boolean algebras.

Research paper thumbnail of Some metalogical properties for infinitary predicate topological logic

We prove completeness, interpolation and omitting types for certain predicate topological logics ... more 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 topological models of a countable theory

Research paper thumbnail of Axiomatizable

We show that for 2 < n + 1 < m, the class Nr n CA m is psuedo elementary, whose elementary that i... more We show that for 2 < n + 1 < m, the class Nr n CA m is psuedo elementary, whose elementary that is not finitely axiomatizable.

Research paper thumbnail of The class of neat reducts is not Boolean closed

Call a class of algebras K Boolean closed if whenever 𝔄∈K and 𝔅≅𝔄 in some Boolean valued extensio... more Call a class of algebras K Boolean closed if whenever 𝔄∈K and 𝔅≅𝔄 in some Boolean valued extension of the universe of sets, then 𝔅∈K. SC, CA, QA and QEA stand for the classes of Pinter’s substitution algebras Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let 1<n≤ω, n<m and K∈{SC,CA,QA,QEA}. We show that the class 𝔑r n K m of all neat n-reducts of algebra in K m (m-dimensional algebras in K) is not Boolean closed. We also show that 𝔑r n CA m and 𝔑r n SC m regarded as concrete categories are not finitely complete (closed under finite limits).