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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
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If A > ITI1 is regular or strong limit, we construct 2" 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. ...
doi:10.1016/0168-0072(87)90005-4
fatcat:4tpnjluwpfcx3mipm4rrt4meoy
Distributions of countable models of theories with continuum many types
[article]
2012
arXiv
pre-print
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We present distributions 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 . ✷ ...
arXiv:1210.4043v1
fatcat:ghimqf6cz5hwrgmdqnrn2qng64
Characterizing all models in infinite cardinalities
2013
Annals of Pure and Applied Logic
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We can ask the question: what kind 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". ...
doi:10.1016/j.apal.2012.10.012
fatcat:32lrhxfaeba65axevlr45rk3um
Forcing isomorphism
[article]
1993
arXiv
pre-print
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Hence, if two 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. ...
arXiv:math/9301208v1
fatcat:baydltafo5bmleniv5w4cpfl2u
An instance of Vaught's conjecture using algebraic logic
[article]
2013
arXiv
pre-print
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In all case we also count the number 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) ) ...
arXiv:1304.0883v1
fatcat:tp2ckxuadbeojdaqf4pzz4cfdq
Recovering function fields from their decomposition graphs
[chapter]
2011
Number Theory, Analysis and Geometry
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We develop the global theory 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. ...
doi:10.1007/978-1-4614-1260-1_24
fatcat:sp6fauxp55cjheqvqwz3islbhu
Isoperimetric inequalities and the Friedlander-Milnor conjecture
[article]
2004
arXiv
pre-print
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discrete, are 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). ...
arXiv:math/0403426v2
fatcat:gudf6vskize63dcb47zedh7lhu
Model theory without choice: Categoricity
[article]
2008
arXiv
pre-print
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Another central result here is, in this context: the number 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. ...
arXiv:math/0504196v3
fatcat:klrhlohghngntbmvjf6vrm6k5i
Combinations of structures
[article]
2016
arXiv
pre-print
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We investigate combinations 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. ...
arXiv:1601.00041v1
fatcat:2ejf63ynkbhodc5tiohp4m6gcm
On Σ^1_1-complete Equivalence Relations on the Generalized Baire Space
[article]
2012
arXiv
pre-print
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Working with uncountable structures 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. ...
arXiv:1209.3932v1
fatcat:if5yx5puivd5tnbb5mrqrj7vpe
Elementary equivalences and accessible functors
2018
Annals of Pure and Applied Logic
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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. ...
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. ...
doi:10.1016/j.apal.2018.03.004
fatcat:ts3bphrykzgyvhhtbx7gqkf6re
Elementary equivalences and accessible functors
[article]
2016
arXiv
pre-print
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We introduce the notion 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. ...
arXiv:1603.02500v1
fatcat:hqd6wmfxmfcklphzcaoqvouw4u
Introduction to twisted commutative algebras
[article]
2012
arXiv
pre-print
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This article is an expository account 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 ...
arXiv:1209.5122v1
fatcat:2dsvs653lff45kxmpeo5e3m3im
Combinations of structures
2018
Известия Иркутского государственного университета: Серия "Математика"
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We investigate combinations 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. ...
doi:10.26516/1997-7670.2018.24.82
fatcat:uoam6x74affg5alxi3zwmtvw6u
Non-computable models of certain first order theories
2017
2017 IEEE 14th International Scientific Conference on Informatics
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We show, that if 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. ...
doi:10.1109/informatics.2017.8327265
fatcat:izfm4x6lp5hgjffxu7raivci7i
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