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The Lascar groups and the first homology groups in model theory

Jan Dobrowolski, Byunghan Kim, Junguk Lee
2017 Annals of Pure and Applied Logic  
THE LASCAR GROUPS AND THE FIRST HOMOLOGY GROUPS IN MODEL THEORY 3 the characterization theorem (Theorem 4.4) of the first homology group and give a criterion for Lstp≡stp.  ...  In Section 5, we state that any connected compact abelian group can appear as the first homology group of the type of a model (Theorem 5.2), which follows from a result by Bouscaren, Lascar, Pillay, and  ...  For the general theory of model theory, of the Lascar groups, and of rosy theories, we refer to [6] , [11] , and [2] , respectively. For the homology theory in model theory, see [4, 3] .  ... 
doi:10.1016/j.apal.2017.06.006 fatcat:eyqhqxru7zfsnf43ufm5j2snqu

The Lascar groups and the 1st homology groups in model theory [article]

Jan Dobrowolski, Byunghan Kim, Junguk Lee
2017 arXiv   pre-print
We also notice that the map factors naturally via a surjection from the 'relativised' Lascar group of the type (which we define in analogy with the Lascar group of the theory) onto the homology group,  ...  We also argue how any abelian connected compact group can appear as the first homology group of the type of a model.  ...  For the general theory of model theory, of the Lascar groups, and of rosy theories, we refer to [6] , [11] , and [2] , respectively. For the homology theory in model theory, see [4, 3] .  ... 
arXiv:1511.03410v3 fatcat:jozdwht6szcipgx27ugvxrmrs4

Lascar groups and the first homology groups of strong types in rosy theories [article]

Junguk Lee
2015 arXiv   pre-print
As a consequence, we show that the first homology groups of strong types in rosy theories have the cardinalities of one or at least 2^_0.  ...  For a rosy theory, we give a canonical surjective homomorphism from a Lascar group over A=^eq(A) to a first homology group of a strong type over A, and we describe its kernel by an invariant equivalence  ...  Lascar group and the first homology groups.  ... 
arXiv:1504.07721v4 fatcat:yxf5tyy3yjhgbjb4e6wjavb4gm

The relativized Lascar groups, type-amalgamation, and algebraicity [article]

Jan Dobrowolski, Byunghan Kim, Alexei Kolesnikov, Junguk Lee
2020 arXiv   pre-print
We apply compact group theory to obtain some model-theoretic results about the relativized Lascar Galois group of a strong type.  ...  Let us recall now the key definitions in the homology theory in model theory.  ...  Let us recall the definitions of the Lascar groups and types. These are well-known notions in model theory.  ... 
arXiv:2004.11309v1 fatcat:y4v63g6sobddnhundoijha6ija

Page 3989 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
To aid in the exposition we develop a variant of Baum’s (M, E, f) model for K-homology. Our model removes the need for Spin® structures in the description of geo- metric K -homology.”  ...  Model theory of groups and automorphism groups ( Blaubeuren, 1995), 115-125, London Math. Soc. Lecture Note Ser., 244, Cambridge Univ. Press, Cambridge, 1997.  ... 

Classifying spaces and the Lascar group [article]

Tim Campion, Greg Cousins, Jinhe Ye
2021 arXiv   pre-print
We show that the Lascar group Gal_L(T) of a first order theory T is naturally isomorphic to the fundamental group π_1(|Mod(T)|) of the classifying space of the category of models of T and elementary embeddings  ...  The Lascar group. In [Las82] , Lascar introduced a notion of a Galois group of a complete first-order theory T , now known as the Lascar group Gal L (T ).  ...  In [GKK13] , a notion of homology of types was defined and in [DKL17] , it was shown that the first homology group of a given type p is given by the abelianization of the relativized Lascar groups.  ... 
arXiv:1808.04915v2 fatcat:nt75jzc725ejnberbhvdcjn5im

Model-Theoretic Algebra With particular emphasis on fields, rings, modules

M. Prest
1993 Bulletin of the London Mathematical Society  
On the other hand, I feel that the author missed an opportunity by not including any account of the development in the last ten years of connections between weak arithmetic and computational complexity  ...  As a whole, this book is highly recommended for the serious student of models of arithmetic.  ...  Two are quite closely related, and they display the breadth and depth of techniques currently in and around the model theory of groups.  ... 
doi:10.1112/blms/25.2.195 fatcat:pnriywskevbfxmguff6z3dewky

Page 4473 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
K.) 2004f:20002 20-06 03C45 03C60 51E24 Tits buildings and the model theory of groups. Papers from the workshop held in Wiirzburg, September 2000. Edited by Katrin Tent.  ...  The main technical point is that the first differential in the spectral sequence is the Steenrod square Sq? of Voevodsky and Brosnan.  ... 

Page 3077 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
3077 higher K-theory groups in a future paper. The third part studies the case when the algebras are no longer unital but H-unital (i.e. unital in a homological sense) as in a paper by M.  ...  It is proved that if G = N x H is a sharply 2-transitive group which is a semidirect product as written where H is the stabilizer of a point and if G is superstable (in the model-theoretic sense) of finite  ... 

On NIP and invariant measures [article]

Ehud Hrushovski, Anand Pillay
2009 arXiv   pre-print
We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of math.LO/0607442.  ...  compact commutative groups in o-minimal expansions of real closed fields.  ...  We conclude the paper by proving that the topologies on J and G/G 00 coincide. Our proof will make use of a little more "theory" some of which is of interest in its own right.  ... 
arXiv:0710.2330v2 fatcat:xfsoqnaaazfajiw3ocn36dnll4

On NIP and invariant measures

Ehud Hrushovski, Anand Pillay
2011 Journal of the European Mathematical Society (Print)  
We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of the paper [16] .  ...  for (definably compact) commutative groups in o-minimal expansions of real closed fields.  ...  A first version of this paper was written in October 2007.  ... 
doi:10.4171/jems/274 fatcat:peg6azkqwzh2nmisi5ireedruu

A classification of 2-chains having 1-shell boundaries in rosy theories [article]

Byunghan Kim, SunYoung Kim, Junguk Lee
2015 arXiv   pre-print
In particular, we prove that in a rosy theory, every 1-shell of a Lascar strong type is the boundary of some 2-chain, hence making the 1st homology group trivial.  ...  We also show that, unlike in simple theories, in rosy theories there is no upper bound on the minimal lengths of 2-chains whose boundary is a 1-shell.  ...  Introduction In [5] , [6] , J. Goodrick, A. Kolesnikov and the first author developed a homology theory for any amenable collection of functors in a very general context.  ... 
arXiv:1503.04564v1 fatcat:k46r7whptfeudbcoilljeetpdm

Amalgamation functors and homology groups in model theory [article]

John Goodrick, Byunghan Kim, Alexei Kolesnikov
2011 arXiv   pre-print
We compute the group H_2 for strong types in stable theories and show that in this context, the class of possible groups H_2 is precisely the profinite abelian groups.  ...  We present definitions of homology groups associated to a family of amalgamation functors. We show that if the generalized amalgamation properties hold, then the homology groups are trivial.  ...  the composition of morphisms, are definable in models of a first-order theory.  ... 
arXiv:1105.2921v1 fatcat:s3mhtpk7qnacppv5lwwhknwxzm

Representation of Subaltern Identity: A Study of Othering in Sea of Poppies

Fehmida Manzoor, Mehwish Ali Khan, Shumaila Mazhar
2020 Global Language Review  
The present study is designed to explore the identity construction/reconstruction in Sea of Poppies. It is investigated in the backdrop of postcolonial theory.  ...  Norman Faircloughs Three-dimensional approach of critical discourse analysis is used to examine the construction and reconstruction of different types of (us/them) identities in the colonial era reflected  ...  It is investigated in the backdrop of postcolonial theory.  ... 
doi:10.31703/glr.2020(v-iv).14 fatcat:k6wpp2wnxregbil4ehxajyedrq

Stable domination and independence in algebraically closed valued fields [article]

Deirdre Haskell, Ehud Hrushovski, Dugald Macpherson
2006 arXiv   pre-print
In Part B, we show that the general theory applies to ACVF. Over a sufficiently rich base, we show that every type is stably dominated over its image in the value group.  ...  In Part A, we develop a general theory of stably dominated types, showing they enjoy an excellent independence theory, as well as a theory of definable types and germs of definable functions.  ...  The first takes place entirely in the value group (so in the theory of divisible ordered abelian groups), but could be encoded into ACVF.  ... 
arXiv:math/0511310v2 fatcat:3iqb3dhn3rd3jep3idxiuln4py
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