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Some highly undecidable lattices

Menachem Magidor, John W. Rosenthal, Mattiyahu Rubin, Gabriel Srour
1990 Annals of Pure and Applied Logic  
Theorems 1.6 and 3.1. Let K be an algebraically closed field of infinite transcendence degree over its prime field, Then the first-order theory of the lattice of algebraically closed subfields of K has the strength of full second-order logic on the set K. That is, loosely speaking, this lattice is as undecidable as possible. In Section 1 we prove this result in characteristic 0 both because the proof is simpler and because the proof illustrates some of the results in Section 2. In Section 3 we
more » ... odify this proof to work in any characteristic. 0168~0072/90/$3.50 0 1990, Elsevier Science Publishers B.V. (North-Holland) U &({Y)), where cl,(B) = cl(A U B). In Section 2 we prove: Theorem 2.13. Let S be a nontrivial, Steinitz exchange system of infinite dimension over 0. Then the first-order theory of the lattice of closed substructures of S is of complexity at least that of second-order .logic on K" (or equivalently, second-order number theory). Section 1 Let K be an algebraically closed field of characteristic 0 and infinite transcendence degree over Q, the rationals. Let k = cl(Q). Let 3 be the lattice of algebraically closed subfields of K. Let 3* consist of 6p together with several parameters, that is, constant symbols for several elements of 3 to be introduced shortly. We first show that _Y* has the logical complexity of second-order logic on K, and then we show how to eliminate the use of these parameters. Let B = {bi : i E Z} be a transcendence basis of K over k. As K is of infinite transcendence degree, K and Z have the same cardinality. Thus, it suffices to show how to translate all sentences of second-order logic on Z into sentences of the first-order theory of 9* (and later on 3). Furthermore, by folklore it suffices to show how to translate into sentences of the first-order theory of 3* only those sentences of second-order logic with quantification over elements of Z and quantification over functions from Z to 1.
doi:10.1016/0168-0072(90)90077-f fatcat:7fx6jjbqhbdoblkeeayaoadura

Economic Integration, Sectoral Diversification, and Exchange Rate Policy in a Developing Economy

Gabriel Srour
2004 IMF Working Papers  
This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. The paper develops a simple three-sector model of a developing country with nominal wage rigidity, in which one sector is thought of as the primary sector and the
more » ... ther two are sectors in which the country can diversify. The paper then analyzes the relationship between the market structure of the nonprimary sectors and equilibrium adjustments to shocks in the primary sector. In particular, the paper examines under what conditions the country should promote one nonprimary sector over another. Among other things, it argues that developing countries should promote those sectors that are more integrated with the outside world. JEL Classification Numbers: E52, F15, F41
doi:10.5089/9781451848083.001 fatcat:ul52pwawxbge7d3tykxiqczpim

Integrating Data Collection Optimization into Pavement Management Systems

Gabriel Bazi, John El Khoury, F. Jordan Srour
2017 Business & Information Systems Engineering  
However, given the distance between the arcs that must be traversed, such routing problems can be reduced to an asymmetric traveling salesman problem (ATSP) (Srour and van de Velde 2013) .  ... 
doi:10.1007/s12599-017-0466-4 fatcat:fefyb2ix4fbcxmm4svnaqsthx4

The Implications of Trade Barriers for Sectoral Diversification and Macroeconomic Stability in Developing Economies

Gabriel Srour
2006 IMF Working Papers  
These results extend those in Srour (2004) .  ...  In that sense, the analysis in Srour (2004) was incomplete. Moreover, the earlier work assumed the law of one price to hold.  ... 
doi:10.5089/9781451863109.001 fatcat:kip5blc4gncizg7d674zcblgza

The notion of independence in categories of algebraic structures, part I: Basic properties

Gabriel Srour
1988 Annals of Pure and Applied Logic  
Communicated by Y. Gurevich Received22Julyl!Bs;revi!sed15May1986 We defme a formula #(lt;#) in a &&-order language L, to be an equation in a category of L&n&uresEiff&anyHinK,andset p={t#(x;uJ;id,u@f} We say that an elementary first+u-der theory T which has the amalgamation property over substructures is equational if every quantiGerⅇ formula is equivalent in T to a boolean fxmhinahn of (qua&&&e) equations in Mod(T), the category of models of T with embedd@s for morphisms. Thus, we develop a
more » ... ry of independence with respect to equations in general categories of strudures, which is similar to the one introduced in stabiity (and actually identical to it in the case of equational theories) but which, in our context, has an algebraic character. The motivation for this work comes largely from the work of Shelah on stable theories. In his investigation of a stable theory T, Shelah showed the existence of an independence relation between the subsets of a model of T which satisfy some natural properties (see axioms 1-C below). This notion was crucial for developing a dimension theory on structures and the proof of structure theorems. However, the notion of a stable theory, and consequently the independence relation introduced by Shelah does not take into consideration the 'algebraic' character of many of the familiar examples of algebra. In particular, it does not take into consideration the existence in such theories of distinguished formulas which play the same role that algebraic equations play in the theory of fields or linear equations in the theory of vector spaces. Our aim in this paper is to show that there is a good notion of a distinguished formula, that we call 'equation', *'This work has been supported by grants from the F.C.A.C. and the N.S.E.R.C. vier Science Publishers B.V. (North-Holland) 186 G. Smir which is a natural generalization of standard equations in algebra (e.g., algebraic equations, linear equations, di&xential equations, etc.). And also that we can de&~ (say, in a given class of structures) an independence relation with respect to a set of 'equations' in very much the same manner algebraic independence is in the class of gelds, or linear independence in the class of vector spaces. the beginning and assume only a naive understanding of relation means. The following are some examples. (a) In the category of fields F with field homomorphisms, we have the notion of independence. More precisely, given fields &c & Ii; c F, we say that independent from I$ over I& if whenever A is a finite set of elements in 4 which is algebraically independent over 6, then A remains . a&bmdly independent over 4. For A, B, C subsets of a Eeld F, write B dam C if (AU B) (the field generated by AU B) is algebraically independent from (AUC)over(A).LetusalsosaythatBisisomorphictoCoverAifthereisa fteld isomorphism from (AU B) onto (AUC) keeping A fixed. Then the relation rl, satisfies the fbllowing properties. 1. (Existence). There exists LEP extending F which contains an isomorphic oapy B' of B over A such that B' dam C. 2. (Monotonicity-transitivity). Giien D c C, B &A C itf B rLD C and B &A D. 3. @cal &aracter). B 4~~ C ifE B 4~~ Co for every finite subset CO of C. 4. (Symmetry). B &A C iff C~Q B. 5. (Stability). (i) Th ere exists COc C such that B &" C aud [CO1 s lB[ + &. (ii) Assumhg B unite, there are at most 2% (actually here at most finitely many) isomorphic copies B' of B over A which are non-isomorphic over C and such that B' &A c. (b) In the category MR of modules over a f&d ring, we have the notion of direct sum over a module. For A, B, C subks of a module M, write B &A C if (AU B) fl (AU C) = (A) ((A) the module generated by A), i.e., if the sum (A U B) + (A UC) is direct over (A). Again, one verifies that the relation & satisks the properties 1-C described above. (c) More generally, in an arbitrary category of L-structures (L a tit-order language) one has the notion of free amalgamation, which is defined as follows: let hi:&+Hi andJ:Hi*H, i=l, 2, be morphisms in Ktithfihl=& Then H (in principle, we should say (H,fi,fi)) is a f&e amalgam of HI and H2 if for any gi :Hi+ G (i = 1,2) with g,hl =g&z, there exists a homomorphism (i.e., a map preserving the atomic formulas) h : H+ G such that I& = gi, i = 1,2. Write(H~,~)~II,(Hs,fi)ifthereexistsgi:H~-,G, i=l,2, andg:G-,Hsuch that g&l =g&z, ggi =t& and G is a free amalgam of HI and Hz over &. e relation & defined above does not satisfy properties 1,2, 3, 5. an elementary class with embeddings for morphisms, which has
doi:10.1016/0168-0072(88)90053-x fatcat:6iubugynsvhj5mpyatlwkt2mby

Práticas diferenciadas de governança corporativa: um estudo sobre a conduta e a performance das firmas brasileiras

Gabriel Srour
2005 Revista Brasileira de Economia  
Sumário: 1. Introdução; 2. Mecanismos de proteção aos minoritários: contratos privados e direito societário; 3. Teoria e metodologia dos testes; 4. Banco de dados e seleção da amostra; 5. resultados; 6. Conclusão.
doi:10.1590/s0034-71402005000400006 fatcat:atgko5xupbfptobtb3sgl2jpfe

Restoration of Outer Retinal Layers After Aflibercept Therapy in Exudative AMD: Prognostic Value

Florence Coscas, Gabriel Coscas, Marco Lupidi, Ali Dirani, Mayer Srour, Oudy Semoun, Catherine Français, Eric H. Souied
2015 Investigative Ophthalmology and Visual Science  
PURPOSE. To evaluate the outer retinal layer (ellipsoid zone [EZ] and external limiting membrane [ELM]) changes following intravitreal aflibercept injections in eyes with treatmentnaïve exudative age-related macular degeneration (eAMD) and to correlate these changes with fluid response and visual improvement. METHODS. A retrospective case series of 50 treatment-naïve eAMD eyes followed-up for 18 months. All patients underwent regular comprehensive ophthalmic examinations. The presence of EZ
more » ... uption, ELM disruption, EZ swelling, subretinal hyper-reflective exudation (SHE), central macular thickness (CMT), cystoid spaces, subretinal fluid, and pigmented epithelium detachment were evaluated by two different retinal specialists at baseline and final visits, and correlated with best corrected visual acuity (BCVA) improvement. RESULTS. At 18 months, BCVA, EZ disruption, ELM disruption, EZ swelling and SHE improved significantly (P ¼ 0.001) at 18 months. Improvement of BCVA showed a statistically significant correlation with ELM restoration (P ¼ 0.018), but not with EZ restoration (P ¼ 0.581). Swelling of the EZ decreased from 72% of the cases at baseline to 30% in 18 months while SHE decreased from 52% to 6% in 18 months (P ¼ 0.001). We observed a statistically significant (P ¼ 0.001) reduction between the baseline and final value of CMT. CONCLUSIONS. Aflibercept is safe and effective in treating exudative AMD with the restoration of the outer retinal layers. Restoration of the EZ is not statistically correlated with the final BCVA, even though persistent EZ changes could be associated with irreversible decrease in vision. On the contrary, the final status of the ELM is directly correlated with final BCVA. Also, baseline changes in outer retinal layers, especially the ELM, appear to predict photoreceptor restoration and final BCVA, and must be comprehensively analyzed to enable and determine a future prognosis.
doi:10.1167/iovs.15-16735 pmid:26114491 fatcat:kxc7x6vae5bd3czar5kuhgpxl4

Prevalence of antibodies to a new histo-blood system: the FORS system

Carlos Jesus, Camilla Hesse, Clara Rocha, Nádia Osório, Ana Valado, Armando Caseiro, António Gabriel, Lola Svensson, Ali-Reza Moslemi, Wafa Abu Siba, Mahmoud A Srour, Cristina Pereira (+3 others)
2016 Blood Transfusion  
In 1987, three unrelated English families were reported with a putative blood subgroup called Apae. Swedish researchers later found evidence leading to abolishment of the Apae subgroup and establishment instead of the FORS blood group system (System 31 - ISBT, 2012). It is important to know the prevalence of antibodies in order to make the best decisions in transfusion medicine. Cells expressing the Forssman saccharide, such as sheep erythrocytes, are needed to detect the anti-Forssman
more » ... The aim of this study was to define the prevalence of human anti-Forssman antibody.
doi:10.2450/2016.0120-16 pmid:27893352 pmcid:PMC5839615 fatcat:gq3o44eksrhelgje44tueqq7yy

Comparison of Macular Choroidal Thickness in Adult Onset Foveomacular Vitelliform Dystrophy and Age-Related Macular Degeneration

Florence Coscas, Nathalie Puche, Gabriel Coscas, Mayer Srour, Catherine Français, Agnes Glacet-Bernard, Giuseppe Querques, Eric H. Souied
2014 Investigative Ophthalmology and Visual Science  
PURPOSE. To compare macular choroidal thickness (MCT) in eyes with adult onset foveomacular vitelliform dystrophy (AOFVD) and eyes with AMD. METHODS. Five groups of 38 eyes each were included in a prospective, observational, comparative study: AOFVD eyes with fluid accumulation; AOFVD fellow eyes without fluid (early stage); advanced exudative (wet) AMD; advanced dry AMD; and healthy normal eyes. All study eyes underwent a comprehensive ophthalmologic examination. Macular choroidal thickness
more » ... measured using enhanced depth imaging optical coherence tomography (EDI-OCT). RESULTS. Subfoveal choroidal thickness (SFCT) in AOFVD with subretinal fluid (325.66 6 85.98 lm) was significantly (P < 0.001) thicker compared with that in exudative AMD (158.55 6 57.87 lm) and in dry AMD (157.53 6 67.08 lm). Also, in AOFVD, the choroid was significantly (P ¼ 0.001) thicker than that in the normal group (255.87 6 87.46 lm). However, in AOFVD, there was no significant difference (P ¼ 0.69) between the SFCT in the study eye and in the fellow eye (317.66 6 90.04 lm). The choroidal thickness at each of the other 12 measured points showed similar results. CONCLUSIONS. This study demonstrates choroidal thickening in AOFVD in contrast with the choroidal thinning observed in advanced AMD. These findings suggest that the pathogenic mechanisms in AOFVD are different from those in exudative AMD. Choroidal thickness measurement could help differentiate the challenging diagnosis between exudative AMD and the advanced stage of AOFVD (with fluid accumulation but without choroidal neovascularization). Keywords: adult onset foveomacular vitelliform dystrophy, age-related macular degeneration (AMD), choroidal neovascularization (CNV), choroidal thickness, enhanced depth imaging (EDI), optical coherence tomography (OCT), pigment epithelial detachment (PED)
doi:10.1167/iovs.13-12931 pmid:24282233 fatcat:vkyalau5ojailf3f3mpdxbjyue

Inflation Targeting under Uncertainty

Gabriel Srour
1999
This paper studies the implications of certain kinds of uncertainty for monetary policy. It first describes the optimum policy rule in a simple model of the transmission mechanism as in Ball and Svensson. It then examines how this rule ought to be modified when there is uncertainty about the parameters, about the time lags, or about the nature of shocks. The paper also discusses the case of a small open economy such as Canada's, with particular attention being given to uncertainty about the weights in a monetary conditions index.
doi:10.34989/tr-85 fatcat:u6xqo33w7bbg7hrcdcqdj5vc5e

Why Do Central Banks Smooth Interest Rates?

Gabriel Srour
2001
currencywhen, on the contrary, caution owing to uncertainty dictates immediate sharp movements in the interest rate, followed by a gradual return to normal, to curb the momentum in public anticipation (Srour  ...  Hence, there is a certain degree of inertia in the conduct of monetary policy (Srour 1999b) . This can explain the intuition in Goodhart's and Freedman's claims (arguments 6 and 7, respectively) .  ... 
doi:10.34989/swp-2001-17 fatcat:bdseb6zrr5esxiyt7ku7ucy7eq

Some Notes on Monetary Policy Rules with Uncertainty

Gabriel Srour
2003
This paper extends the analysis in Srour (1999, henceforth referred to as [S]).  ...  Under some conditions, for instance, it can be shown that inflation targeting with commitment is equivalent to price-level targeting without commitment (see Srour 2001 ).  ... 
doi:10.34989/swp-2003-16 fatcat:wwqmspioyvhmvbgbbgecgu7h2e

The Monetary Transmission Mechanism at the Sectoral Level

Jean Farès, Gabriel Srour
2001
This paper relies on simple vector autoregressions to investigate the monetary transmission mechanism in broad sectors of the Canadian economy. Two types of disaggregation are considered: one at the level of final expenditures, and one at the level of production. At the level of final expenditures, it is found that a monetary contraction affects exports relatively quickly, and it affects investment much more substantially than the consumption of goods, while it does not seem to affect services.
more » ... Not surprisingly, durables respond much more substantially than semi-durables to a monetary contraction, while non-durables do not respond significantly. At the level of production, following a monetary contraction, construction reaches the trough of the cycle first, although, cumulatively, manufacturing reacts twice as strongly. The response of the service sector is significant, but it lags manufacturing.
doi:10.34989/swp-2001-27 fatcat:5wfunzuhljhtbaq2tyeekopvye

Price-Level versus Inflation Targeting in a Small Open Economy

Gabriel Srour
2001
This paper compares two types of monetary policy: price-level targeting and inflation targeting. It reviews recent arguments that favour price-level targeting, and examines how certain factors, such as the nature of the shocks affecting the economy and the degree to which agents are forward-looking, bear upon the arguments. The paper then extends the analysis to a small open economy such as Canada's, and considers whether it is practical for this country to pursue price-level targets if its
more » ... nant trading partner, the United States, allows the price level to drift.
doi:10.34989/swp-2001-24 fatcat:t5cb44bwerd2vd5444ctz2r7hy

The Sale of Durable Goods by a Monopolist in a Stochastic Environment

Gabriel Srour
1998
Figures 1 and 2 depict the impulse response of price and output (in percentage terms) prices down during a boom (see Srour 1997b) .  ...  constant, the condition becomes (1 )b t+1 b t , i.e. demand must not drop by more than the depreciation rate per cent, which i s o b viously satised if demand is rising in time (b t+1 b t ). 9 See Srour  ...  By lemma 1 , D t D t ( D ) satises the rst order condition 29 A rigorous proof can be found in Srour, 1997a. 23 Rearranging the elements yields an expression for D t D t (D) as claimed, while the expression  ... 
doi:10.34989/swp-1998-18 fatcat:dhumz45ofrb7ni7lwalzwsmfl4
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