COFINALITY QUANTIFIERS IN ABSTRACT ELEMENTARY CLASSES AND BEYOND

被引：0

作者：

Boney, Will ^{[1
]}

机构：

[1] Texas State Univ, Math Dept, 601 Univ Dr, San Marcos, TX 78666 USA

来源：

JOURNAL OF SYMBOLIC LOGIC | 2023年

基金：

美国国家科学基金会;

关键词：

Abstract Elementary Classes; cofinality quantifiers; generalized quantifiers; Skolemization;

D O I：

10.1017/jsl.2023.34

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The cofinality quantifiers were introduced by Shelah as an example of a compact logic stronger than first-order logic. We show that the classes of models axiomatized by these quantifiers can be turned into an Abstract Elementary Class by restricting to positive and deliberate uses. Rather than using an ad hoc proof, we give a general framework of abstract Skolemizations. This method gives a uniform proof that a wide rang of classes are Abstract Elementary Classes.

引用

页数：15

共 18 条

[1]

Baldwin, 2009, U LECT SERIES, V50

[2] ⊥N as an abstract elementary class [J].

Baldwin, John T. ;

Eklof, Paul C. ;

Trlifaj, Jan .

ANNALS OF PURE AND APPLIED LOGIC, 2007, 149 (1-3) :25-39

[3]

Baldwin JT, 2017, BEYOND FIRST ORDER MODEL THEORY, P327

[4]

Barwise Jon., 1982, Handbook of mathematical logic

[5]

Boney W., 2019, B POLISH ACAD SCI MA, V67, P1

[6]

Boney W, 2017, BEYOND FIRST ORDER MODEL THEORY, P353

[7] μ-Abstract elementary classes and other generalizations [J].

Boney, Will ;

Grossberg, Rami ;

Lieberman, Michael ;

Rosicky, Jiri ;

Vasey, Sebastien .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (09) :3048-3066

[8] AN EXPOSITION OF THE COMPACTNESS OF L(Qcf) [J].

Casanovas, Enrique ;

Ziegler, Martin .

BULLETIN OF SYMBOLIC LOGIC, 2020, 26 (3-4) :212-218

[9] UNIVERSAL THEORIES AND COMPACTLY EXPANDABLE MODELS [J].

Casanovas, Enrique ;

Shelah, Saharon .

JOURNAL OF SYMBOLIC LOGIC, 2019, 84 (03) :1215-1223

[10]

Chang C. C., 2012, Model Theory, Vthird

← 1 2 →