A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
The Lascar Group and the Strong Types of Hyperimaginaries

2013
*
Notre Dame Journal of Formal Logic
*

This is an expository note on

doi:10.1215/00294527-2143916
fatcat:yo6veora5befhjeppvdjpfvd5y
*the**Lascar**group*. We also study*the**Lascar**group*over*hyperimaginaries*,*and*make some new observations on*the**strong**types*over those. ... In particular we show that in a simple theory, Ltp ≡ stp in real context implies that for*hyperimaginary*context. ... Notably in [9] [1], a new look on*the**Lascar**group*is given,*and*using compact Lie*group*theory*Lascar**and*Pillay proved that any bounded*hyperimaginary*is interdefinable with a sequence*of*finitary bounded ...##
###
Automorphism groups over a hyperimaginary
[article]

2021
*
arXiv
*
pre-print

On

arXiv:2106.09200v1
fatcat:b2l3twzqzngwnie2hz57befi2u
*the*other, we extend Newelski's Theorem in "*The*diameter*of*a*Lascar**strong**type*" [12] that 'a G-compact theory over a set has a uniform bound for*the**Lascar*distances' to*the**hyperimaginary*context ... We further extend a result that*the*orbit equivalence relation under a closed subgroup*of**the**Lascar**group*is*type*-definable. ... Namely we investigate*the*Kim-Pillay*group**and**the*Shelah*group*,*and*corresponding notions*of*Kim-Pillay*types**and*Shelah*strong**types*, over a*hyperimaginary*. ...##
###
Elimination of Hyperimaginaries and Stable Independence in Simple CM-Trivial Theories

2013
*
Notre Dame Journal of Formal Logic
*

In a simple CM-trivial theory every

doi:10.1215/00294527-2143970
fatcat:tf2snizezjgxliqdu36xejjb4a
*hyperimaginary*is interbounded with a sequence*of*finitary*hyperimaginaries*. ... Moreover, such a theory eliminates*hyperimaginaries*whenever it eliminates finitary*hyperimaginaries*. In a supersimple CM-trivial theory,*the*independence relation is stable. ... Since h ∈ bdd(c), equality*of**Lascar**strong**types*over c refines equality*of**Lascar**strong**types*over h,*and**the*class*of*a modulo*the*former is clearly in dcl(ac). ...##
###
Normal hyperimaginaries
[article]

2013
*
arXiv
*
pre-print

We introduce

arXiv:1112.2049v3
fatcat:uryyxpa2ljfhhfyjzgwtvpk2ua
*the*notion*of*normal*hyperimaginary**and*we develop its basic theory. ... In*the*second part, we show that all closed sets in Kim-Pillay spaces are equivalent to*hyperimaginaries**and*we use this to introduce an approximation*of*φ-*types*for bounded*hyperimaginaries*. ... It is also called*the*Kim-Pillay equivalence relation*and*its classes are called KP-*strong**types*.*The*set*of*all KP-classes*of*α-tuples is C α /KP. ...##
###
The Group Configuration in Simple Theories and its Applications

2002
*
Bulletin of Symbolic Logic
*

*of*pseudolinearity

*and*local modularity.The proof necessitated an extension

*of*

*the*model-theoretic framework to includealmost

*hyperimaginaries*,

*and*

*the*study ofpolygroups. ... theorem, or, in

*the*ω-categorical case,

*the*characterization

*of*

*the*forking geometry

*of*a finitely based non-trivial locally modular regular

*type*as projective geometry over a finite field

*and*

*the*equivalence ... Two ultraimaginaries a R

*and*b R have

*the*same (

*Lascar*

*strong*)

*type*over a

*hyperimaginary*c if there are representatives which do. ...

##
###
Group configurations and germs in simple theories

2002
*
Journal of Symbolic Logic (JSL)
*

This is

doi:10.2178/jsl/1190150301
fatcat:i5xr27zoqvff7i6qmv4m5kzwte
*the*first step towards*the*proof*of**the**group*configuration theorem for simple theories, which is completed in [3]. ... We develop*the*theory*of*germs*of*generic functions in simple theories. ... set*of*all possible extensions*of**the*graph to a*Lascar**strong**type*over*the*parameter. ...##
###
Page 757 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

*The*conclusion is a set

*of*four open questions,

*the*last one asking whether, in a simple theory,

*the*

*Lascar*

*strong*

*type*is nothing more than

*the*

*strong*

*type*,

*and*a

*hyperimaginary*nothing more than a (possibly ... Another corollary is

*the*same property over an arbitrary set

*of*parameters inside a

*Lascar*

*strong*

*type*(if a

*and*b have

*the*same

*type*over a model containing A, then they have

*the*same

*Lascar*

*strong*

*type*...

##
###
Supersimple Theories
[chapter]

2000
*
Simple Theories
*

In fact

doi:10.1007/978-94-017-3002-0_5
fatcat:clqqg5w64vfqhctaq2aj7ltb4a
*the*reader should note that our proof also yields*the*equality*of**Lascar**strong**type*with*strong**type*in low simple theories. ... consider*type*-definable equivalence relations with a small number*of*classes (corresponding to*Lascar**strong**types*). ...##
###
Generalized amalgamation and homogeneity
[article]

2016
*
arXiv
*
pre-print

In particular, this adapts a result

arXiv:1603.09694v3
fatcat:gqrza3hkeneonix5qbd77wymde
*of*Koponen for binary homogeneous structures to arbitrary ones without binary relations. ... Furthermore, we point out a relation between generalized amalgamation, triviality*and*quantifier elimination in simple theories. ... This motivates*the*definition*of*a*Lascar**strong**type*: A*type*over which*the*Independence Theorem holds. We denote*the**Lascar**strong**type**of*a over A by Lstp(a/A). ...##
###
Supersimple theories

2000
*
Journal of The American Mathematical Society
*

In fact

doi:10.1090/s0894-0347-00-00350-7
fatcat:c7drkevsbjcylpghdoi3wrtu6m
*the*reader should note that our proof also yields*the*equality*of**Lascar**strong**type*with*strong**type*in low simple theories. ... consider*type*-definable equivalence relations with a small number*of*classes (corresponding to*Lascar**strong**types*). ...##
###
APPLICATIONS OF THE GROUP CONFIGURATION THEOREM IN SIMPLE THEORIES

2003
*
Journal of Mathematical Logic
*

We reconstruct

doi:10.1142/s0219061303000261
fatcat:kkgqzew6andhvknpeqnzqk5xlq
*the**group*action in*the**group*configuration theorem. ... We apply it to show that in an ω-categorical theory a finitely based pseudolinear regular*type*is locally modular,*and**the*geometry associated to a finitely based locally modular regular*type*is projective ... This coincides with*the*definitions for*hyperimaginaries*; two almost*hyperimaginaries*have*the*same (*Lascar**strong*)*type*over c if*and*only if they are conjugate under a (*strong*) c-automorphism. ...##
###
Plus ultra
[article]

2014
*
arXiv
*
pre-print

Finally, we prove some uniform versions

arXiv:1201.1114v4
fatcat:e6nek4gii5hbzkwlfy2naar5mu
*of**the*weak canonical base property. ... We define a reasonably well-behaved class*of*ultraimaginaries, i.e. classes modulo invariant equivalence relations, called tame,*and*establish some basic simplicity-theoretic facts. ...*of**Lascar**strong**types*over A*of*real tuples*of*length κ, since equality*of**Lascar**strong**type*over A is*the*finest bounded A-invariant equivalence relation. ...##
###
Bounded ultraimaginary independence and its total Morley sequences
[article]

2022
*
arXiv
*
pre-print

sequence over A if

arXiv:2201.03631v1
fatcat:qdlpt3bnozbjlha2rvr52pvmai
*and*only if whenever I*and*I' have*the*same*Lascar**strong**type*over A, I*and*I' are related by*the*transitive, symmetric closure*of**the*relation 'J+K is A-indiscernible.' ... set*of**hyperimaginaries*A*and*ultraimaginaries b*and*c, there is a b' ≡_A b such that b' _Amu c). ... Another appealing aspect*of*ultraimaginaries is that they characterize*Lascar**strong**type*in*the*same way that*hyperimaginaries*characterize Kim-Pillay*strong**type*. ...##
###
On almost orthogonality in simple theories

2004
*
Journal of Symbolic Logic (JSL)
*

fixing Σ generically In case p is Σ-internal

doi:10.2178/jsl/1082418533
fatcat:m55czfzw6jdvpjlse6zenhewgq
*and*T is stable, this is*the*binding*group**of*p over Σ. ... If p is a possibly*hyperimaginary**Lascar**strong**type*, almost Σ-internal, but almost orthogonal to Σ ω , then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts on p while ... to a*Lascar**strong**type*). ...##
###
Rigidity, internality and analysability

2014
*
Fundamenta Mathematicae
*

We prove a version

doi:10.4064/fm224-1-3
fatcat:vppumaiuvjcmpotj664327yr5e
*of*Hrushovski's Socle Lemma for rigid*groups*in an arbitrary simple theory. 2000 Mathematics Subject Classification. 03C45. ... Let G be a rigid abelian*group**of*finite SU-rank,*and*p a*Lascar**strong*G-*type**of*finite stabilizer. Then p is almost internal in*the*set Σ*of*all*types**of*SU-rank one. ... More generally, Chatzidakis proves*the*following two facts (she works in a simple theory with elimination*of**hyperimaginaries**and**the*family Σ*of*all non locally modular (*Lascar*)*strong**types**of*SU-rank ...
« Previous

*Showing results 1 — 15 out of 67 results*