CONSTANT EXPANSION OF THEORIES AND THE NUMBER OF COUNTABLE MODELS

被引：0

作者：

Sembyuly, Baizhanov Bektur ^{[1
,2
]}

Asylbekovich, Umbetbayev Olzhas ^{[1
,3
]}

机构：

[1] Inst Math & Math Modeling, 28 Shevchenko St, Alma Ata 050010, Kazakhstan

[2] SDU Univ, 1-1 Abylai khan St, Kaskelen 040900, Kazakhstan

[3] Kazakh British Tech Univ, 59 Tole Bi St, Alma Ata 050000, Kazakhstan

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2023年 / 20卷 / 02期

关键词：

small theory; the number of countable models; expansion by constants; non-orthogonality of types; ordered structures;

D O I：

10.33048/semi.2023.20.064

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The present paper is dedicated to the method of constant expansion of a complete theory for studying its number of countable models. This paper aims to rehabilitate the method of constant expansion by demonstrating its continued relevance and its potential for use in counting the number of countable models. The main result reveals that the question of reducing the number of countable models from the continuum to a countable number by a constant expansion of a theory remains unanswered, contrary to previous beliefs.

引用

页码：1037 / 1051

页数：15

共 50 条

[1] THEORIES WITH A FINITE NUMBER OF COUNTABLE MODELS
WOODROW, RE
[J]. JOURNAL OF SYMBOLIC LOGIC, 1978, 43 (03) : 442 - 455
[2] On the number of countable models of stable theories
Tanovic, P
[J]. FUNDAMENTA MATHEMATICAE, 2001, 169 (02) : 139 - 144
[3] STABLE THEORIES, PSEUDOPLANES AND THE NUMBER OF COUNTABLE MODELS
PILLAY, A
[J]. ANNALS OF PURE AND APPLIED LOGIC, 1989, 43 (02) : 147 - 160
[4] ON THEORIES HAVING A FINITE NUMBER OF NONISOMORPHIC COUNTABLE MODELS
TSUBOI, A
[J]. JOURNAL OF SYMBOLIC LOGIC, 1985, 50 (03) : 806 - 808
[5] THEORIES WITH A FINITE NUMBER OF COUNTABLE MODELS - PRELIMINARY-REPORT
WOODROW, RE
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (05): : A497 - A497
[6] NUMBER OF COUNTABLE MODELS
MORLEY, M
[J]. JOURNAL OF SYMBOLIC LOGIC, 1970, 35 (01) : 14 - &
[7] NUMBER OF COUNTABLE MODELS
PILLAY, A
[J]. JOURNAL OF SYMBOLIC LOGIC, 1978, 43 (03) : 492 - 496
[8] NUMBER OF COUNTABLE MODELS
PILLAY, A
[J]. JOURNAL OF SYMBOLIC LOGIC, 1979, 44 (03) : 456 - 456
[9] COUNTABLE MODELS AND UNIONS OF THEORIES
TSUBOI, A
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1986, 38 (03) : 501 - 508
[10] COUNTABLE MODELS OF STABLE THEORIES
PILLAY, A
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 89 (04) : 666 - 672

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