共查询到20条相似文献,搜索用时 46 毫秒
1.
We show that the complete first order theory of an MV algebra has $2^{\aleph _0}$ countable models unless the MV algebra is finitely valued. So, Vaught's Conjecture holds for all MV algebras except, possibly, for finitely valued ones. Additionally, we show that the complete theories of finitely valued MV algebras are $2^{\aleph _0}$ and that all ω‐categorical complete theories of MV algebras are finitely axiomatizable and decidable. As a final result we prove that the free algebra on countably many generators of any locally finite variety of MV algebras is ω‐categorical. 相似文献
2.
A. S. Morozov 《Algebra and Logic》1995,34(4):242-248
It is proved that there exists no relationship between isomorphism types of the ordinary and recursive automorphism groups of recursive models and the property of being decidable for these models. Moreover, we show that all isomorphism types of recursive automorphism groups can be realized in a single (up to isomorphism) decidable countably categorical model. Taking account of the action of a group on the universe of the model makes it possible to distinguish between the classes of groups for decidable and all the recursive models.Translated fromAlgebra i Logika, Vol. 34, No. 4, pp. 437–447, July-August, 1995. 相似文献
3.
Complexity of Categorical Theories with Computable Models 总被引:1,自引:0,他引:1
M. Lerman and J. Scmerl specified some sufficient conditions for computable models of countably categorical arithmetical theories to exist. More precisely, it was shown that if T is a countably categorical arithmetical theory, and the set of its sentences beginning with an existential quantifier and having at most n+1 alternations of quantifiers is
n+1
0
for any n, then T has a computable model. J. Night improved this result by allowing certain uniformity and omitting the requirement that T is arithmetical. However, all of the known examples of theories of0-categorical computable models had low level of algorithmic complexity, and whether there are theories that would satisfy the above conditions for sufficiently large n was unknown. This paper will include such examples. 相似文献
4.
Olivia Caramello 《Logica Universalis》2014,8(2):261-281
We present a topos-theoretic interpretation of (a categorical generalization of) Fraïssé’s construction in Model Theory, with applications to homogeneous models and countably categorical theories. 相似文献
5.
S. V. Sudoplatov 《Algebra and Logic》2004,43(1):62-69
A syntactic characterization is furnished for the class of elementary complete theories with finitely many countable models, which is the analog of a known theorem by Ryll-Nardzewski on countably categorical theories, and is based on classifying the theories by Rudin-Keisler quasiorders and distribution functions of a number of models limit over types. 相似文献
6.
P. E. Alaev 《Siberian Advances in Mathematics》2008,18(4):227-241
We study countable Boolean algebras with finitely many distinguished ideals (countable I-algebras) whose elementary theory is countably categorical, and autostable I-algebras which form their subclass. We propose a new characterization for the former class that allows to answer a series of questions about the structure of countably categorical and autostable I-algebras. 相似文献
7.
B. Sh. Kulpeshov 《Siberian Mathematical Journal》2016,57(4):606-617
We completely describe countably categorical weakly o-minimal theories of finite convexity rank. 相似文献
8.
A. Ivanov 《Siberian Advances in Mathematics》2010,20(2):75-82
We give an example of a countably categorical theory which is not G-compact. The countable model of this theory does not have
AZ-enumerations. 相似文献
9.
Vincent Astier 《Archive for Mathematical Logic》2008,47(4):327-340
We characterize elementary equivalences and inclusions between von Neumann regular real closed rings in terms of their boolean
algebras of idempotents, and prove that their theories are always decidable. We then show that, under some hypotheses, the
map sending an L-structure R to the L-structure of definable functions from R
n
to R preserves elementary inclusions and equivalences and gives a structure with a decidable theory whenever R is decidable. We briefly consider structures of definable functions satisfying an extra condition such as continuity.
相似文献
10.
Studying the model-theoretic properties that are preserved under expansion of the models of countably categorical weakly o-minimal theories of finite convexity rank with convex unary predicates, we show that countable categoricity and convexity rank are among these properties. 相似文献
11.
E. A. Palyutin 《Algebra and Logic》2005,44(5):326-335
A question is studied as to which properties (classes) of elementary theories can be defined via generalized stability. We
present a topological account of such classes. It is stated that some well-known classes of theories, such as strongly minimal,
o-minimal, simple, etc., are stably definable, whereas, for instance, countably categorical, almost strongly minimal, ω-stable
ones, are not.
__________
Translated from Algebra i Logika, Vol. 44, No. 5, pp. 583–600, September–October, 2005.
Supported by RFBR grant Nos. 02-01-00540 and 05-01-00411, and by the Council for Grants (under RF President) and State Aid
of Fundamental Science Schools, project NSh-2069.2003.1. 相似文献
12.
13.
Regina Aragn 《Mathematical Logic Quarterly》2003,49(3):260-276
We describe the countably saturated models and prime models (up to isomorphism) of the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal such that the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal such that the supremum of the ideal exists. We prove that there are infinitely many completions of the theory of Boolean algebras with a distinguished ideal that do not have a countably saturated model. Also, we give a sufficient condition for a model of the theory TX of Boolean algebras with distinguished ideals to be elementarily equivalent to a countably saturated model of TX. 相似文献
14.
We consider the sets definable in the countable models of a weakly o‐minimal theory T of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic (hence T is p‐ω‐categorical), in other words when each of these definable sets admits, if infinite, an infinite coinfinite definable subset. We show that this is true if and only if T has no infinite definable discrete (convex) subset. We examine the same problem among arbitrary theories of mere linear orders. Finally we prove that, within expansions of Boolean lattices, every weakly o‐minimal theory is p‐ω‐categorical. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
V. Yu. Popov 《Siberian Mathematical Journal》2001,42(6):1132-1141
For every proper semigroup variety X, there exists a semigroup variety Y satisfying the following three conditions: (1) Y covers X, (2) if X is finitely based then so is Y, and (3) the equational theory of X is decidable if and only if so is the equational theory of Y. If X is an arbitrary semigroup variety defined by identities depending on finitely many variables and such that all periodic groups of X are locally finite, then one of the following two conditions holds: (1) all nilsemigroups of X are locally finite and (2) X includes a subvariety Y whose equational theory is undecidable and which has infinitely many covering varieties with undecidable equational theories. 相似文献
16.
E. A. Palyutin 《Siberian Mathematical Journal》2011,52(6):1056-1064
17.
Let G be a finite group. We prove that the theory af abelian-by-G groups is decidable if and only if the theory of modules over the group ring ?[G] is decidable. Then we study some model theoretic questions about abelian-by-G groups, in particular we show that their class is elementary when the order of G is squarefree. Mathematics Subject Classification: 03C60, 03B25. 相似文献
18.
M. H. Albert 《Algebra Universalis》1996,36(4):467-482
We prove that a varietyV which is locally finite, finitely generated, congruence permutable and of finite type, and whose subdirectly irreducible algebras are all either abelian or linear type 3 above the monolith is finitely decidable if and only if the theory of the finite abelian algebras inV is decidable.Presented by R. McKenzie. 相似文献
19.
It is shown that a variety generated by a nilpotent A-loop has a decidable equational (quasiequational ) theory. Thereby the question posed by A. I. Mal’tsev in [6] is answered in the negative, and moreover, a finitely presented nilpotent A-loop has a decidable word problem. 相似文献
20.
Tapani Hyttinen 《Mathematical Logic Quarterly》2004,50(1):77-98
We generalize the result of non‐finite axiomatizability of totally categorical first‐order theories from elementary model theory to homogeneous model theory. In particular, we lift the theory of envelopes to homogeneous model theory and develope theory of imaginaries in the case of ω‐stable homogeneous classes of finite U‐rank. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献