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Existence of many L∞,λ-equivalent, non- isomorphic models of T of power λ

1987
*
Annals of Pure and Applied Logic
*

If A > ITI1 is regular or strong limit, we construct 2"

doi:10.1016/0168-0072(87)90005-4
fatcat:4tpnjluwpfcx3mipm4rrt4meoy
*non*-*isomorphic*, pairwise*L*", -*equivalent**models**of**T**of**power*A, which are reducts*of**models**of*TI. ... Note, however, that the proof applies to the class*of**models**of**T*,*T*(superstable but) with dop or otop and even to appropriate*non*-elementary classes as well. ... Introduction This paper has a place in two lines*of*research:*existence**of**L*,,*-*equivalent**non*-*isomorphic**models**of**power*A and classification theory. On the history*of*construction*of**L*. ...##
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Distributions of countable models of theories with continuum many types
[article]

2012
*
arXiv
*
pre-print

We present distributions

arXiv:1210.4043v1
fatcat:ghimqf6cz5hwrgmdqnrn2qng64
*of*countable*models*and correspondent structural characteristics*of*complete theories with continuum*many*types: for prime*models*over finite sets relative to Rudin-Keisler preorders ... , for limit*models*over types and over sequences*of*types, and for other countable*models**of*theory. ... Since the process*of*extension*of**models*M p by continuum*many**models*M q can be continued unboundedly*many*times, there are continuum*many*pairwise*non*-*isomorphic*limit*models*, i. e.,*L*(*T*) = 2 ω . ✷ ...##
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Characterizing all models in infinite cardinalities

2013
*
Annals of Pure and Applied Logic
*

We can ask the question: what kind

doi:10.1016/j.apal.2012.10.012
fatcat:32lrhxfaeba65axevlr45rk3um
*of*a logic*L*is needed to characterize all*models**of*cardinality κ (in a finite vocabulary) up to*isomorphism*by their*L*-theories? ... In other words: for which logics*L*it is true that if any*models*A and B*of*cardinality κ satisfy the same*L*-theory then they are*isomorphic*? ... Acknowledgements This article is based on the author's Ph.D. thesis titled "Characterizing All*Models*in Infinite Cardinalities". ...##
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Forcing isomorphism
[article]

1993
*
arXiv
*
pre-print

Hence, if two

arXiv:math/9301208v1
fatcat:baydltafo5bmleniv5w4cpfl2u
*models**of*a classifiable theory*of**power*lambda are*non*-*isomorphic*, they are*non*-*isomorphic*after a lambda-complete forcing. ... In particular, we show that*non*-*isomorphism**of**models**of*a classifiable theory need not be preserved by ccc forcings. ... That is, if two*models**of*a classifiable theory*of**power**λ*are*non*-*isomorphic*, they remain*non*-*isomorphic*after a*λ*-complete forcing. ...##
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An instance of Vaught's conjecture using algebraic logic
[article]

2013
*
arXiv
*
pre-print

In all case we also count the number

arXiv:1304.0883v1
fatcat:tp2ckxuadbeojdaqf4pzz4cfdq
*of**non**isomorphic**models*omitting < covK*many**non*isolated types (the latter is the least cardinal such that the Baire Category theorem fails and also the largest cardinal ... We show that the*equivalence*relation induced by such (indistinguishable)*models*is a Borel subset*of*the product*of*the Stone Polish space (consisting*of*ultarfilters corresponding to*models*) with itself ... Suppose that*T*is a theory, |*T*| =*λ*,*λ*regular, then there*exist**models*M i : i < χ =*λ*2, each*of*cardinality*λ*, such that if i(1) = i(2) < χ, a i(*l*) ∈ |M i(*l*) |,*l*= 1, 2,, tp(ā*l*(1) ) = tp(ā*l*(2) ) ...##
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Recovering function fields from their decomposition graphs
[chapter]

2011
*
Number Theory, Analysis and Geometry
*

We develop the global theory

doi:10.1007/978-1-4614-1260-1_24
fatcat:sp6fauxp55cjheqvqwz3islbhu
*of*a strategy to tackle a program initiated by Bogomolov in 1990. ... program aims at giving a group theoretical recipe by which one can reconstruct function fields K|k with td(K|k) > 1 and k algebraically closed from the maximal pro-abelian-by-central Galois group Π c K*of*... Hence finally ε is a*power**of*the characteristic exponent*of*k and*l*.*Equivalently*, ı is a Frobenius twist*of*ı. ...##
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Isoperimetric inequalities and the Friedlander-Milnor conjecture
[article]

2004
*
arXiv
*
pre-print

discrete, are

arXiv:math/0403426v2
fatcat:gudf6vskize63dcb47zedh7lhu
*equivalent*to the*existence**of*an isoperimetric inequality in the homological bar complex*of*G(F), where F is the algebraic closure*of*a finite field. ... We prove that Friedlander's generalized*isomorphism*conjecture on the cohomology*of*algebraic groups, and hence the*Isomorphism*Conjecture for the cohomology*of*the complex algebraic Lie group G(C) made ... Identifying the*l*th -*power*roots*of*unity in F p with Z/*l*∞ , one gets an injection Z/*l*∞ → F × p such that (Z/*l*∞ ) r →*T*(F p ) induces*isomorphism*on H * (−, Z/*l*). ...##
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Model theory without choice: Categoricity
[article]

2008
*
arXiv
*
pre-print

Another central result here is, in this context: the number

arXiv:math/0504196v3
fatcat:klrhlohghngntbmvjf6vrm6k5i
*of**models**of*a countable first order*T**of*cardinality aleph_alpha is either >=|alpha| for every aleph_\alpha or it has a small upper bound (close ... We prove Los conjecture = Morley theorem in ZF, with the same characterization (*of*first order countable theories categorical in aleph_alpha for some (*equivalently*for every) ordinal alpha>0. ... classes (c) the number*of**models**of**T*in µ up to*isomorphism*is equal to the number*of*E*T*,µ -*equivalence*classes. ...##
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Combinations of structures
[article]

2016
*
arXiv
*
pre-print

We investigate combinations

arXiv:1601.00041v1
fatcat:2ejf63ynkbhodc5tiohp4m6gcm
*of*structures by families*of*structures relative to families*of*unary predicates and*equivalence*relations. ... The notions*of*e-spectra are introduced and possibilities for e-spectra are described. ... As usual we denote by I(*T*,*λ*) the number*of*pairwise*non*-*isomorphic**models**of**T*having the cardinality*λ*. ...##
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On Σ^1_1-complete Equivalence Relations on the Generalized Baire Space
[article]

2012
*
arXiv
*
pre-print

Working with uncountable structures

arXiv:1209.3932v1
fatcat:if5yx5puivd5tnbb5mrqrj7vpe
*of*fixed cardinality, we investigate the complexity*of*certain*equivalence*relations and show that if V =*L*, then*many**of*them are \Sigma^1_1-complete, in particular ... the*isomorphism*relation*of*dense linear orders. ... The research was partially supported by the Academy*of*Finland through its grant WBS 1251557 and the second author was funded by the Science Foundation*of*the University*of*Helsinki. ...##
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Elementary equivalences and accessible functors

2018
*
Annals of Pure and Applied Logic
*

This notion specializes to

doi:10.1016/j.apal.2018.03.004
fatcat:ts3bphrykzgyvhhtbx7gqkf6re
*L*∞*λ*-*equivalence*and*L*∞*λ*-elementary embedding for categories*of*structures in a language*of*arity less than*λ*, and interacts well with functors and*λ*-directed colimits. ... We introduce the notion*of**λ*-*equivalence*and*λ*-embeddings*of*objects in suitable categories. ... Karp's theorem, however, equates*L*∞*λ*-*equivalence**of*structures with the*existence**of*a set*of*partial*isomorphisms*satisfying certain extension properties. ...##
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Elementary equivalences and accessible functors
[article]

2016
*
arXiv
*
pre-print

We introduce the notion

arXiv:1603.02500v1
fatcat:hqd6wmfxmfcklphzcaoqvouw4u
*of**λ*-*equivalence*and*λ*-embeddings*of*objects in suitable categories. ... This notion specializes to L_∞*λ*-*equivalence*and L_∞*λ*-elementary embedding for categories*of*structures in a language*of*arity less than*λ*, and interacts well with functors and*λ*-directed colimits. ... Karp's theorem, however, equates*L*∞*λ*-*equivalence**of*structures with the*existence**of*a set*of*partial*isomorphisms*satisfying certain extension properties. ...##
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Introduction to twisted commutative algebras
[article]

2012
*
arXiv
*
pre-print

This article is an expository account

arXiv:1209.5122v1
fatcat:2dsvs653lff45kxmpeo5e3m3im
*of*the theory*of*twisted commutative algebras, which simply put, can be thought*of*as a theory for handling commutative algebras with large groups*of*linear symmetries ... The third part develops some basic properties*of*twisted commutative algebras from the perspective*of*classical commutative algebra and summarizes some*of*the results*of*the authors. ... The theorem that H M belongs to Q[*t*, e*t*] can be stated*equivalently*using differential equations: it amounts to the*existence**of*a polynomial p, whose roots are*non*-negative integers, such that p(d/dt ...##
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Combinations of structures

2018
*
Известия Иркутского государственного университета: Серия "Математика"
*

We investigate combinations

doi:10.26516/1997-7670.2018.24.82
fatcat:uoam6x74affg5alxi3zwmtvw6u
*of*structures by families*of*structures relative to families*of*unary predicates and*equivalence*relations. ... not approximate infinitely*many*n-types for n ∈ ω. ... As usual we denote by I(*T*,*λ*) the number*of*pairwise*non*-*isomorphic**models**of**T*having the cardinality*λ*. ...##
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Non-computable models of certain first order theories

2017
*
2017 IEEE 14th International Scientific Conference on Informatics
*

We show, that if

doi:10.1109/informatics.2017.8327265
fatcat:izfm4x6lp5hgjffxu7raivci7i
*T*is a first order theory with at least one uncountable Stone space then*T*has a countable*model*not*isomorphic*to any D-presented one. ... We also show that there is a countable ℵ0-categorical structure in a finite language which is not*isomorphic*to any D-presented structure; in addition, there*exists*a consistent first order theory in a ... Suppose H is an uncountable family*of*pairwise*non*-*isomorphic*countable*L*-structures. ...
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