Topological model theory with an interior operator: Consistency properties and back — and forth arguments

1981 ◽  
Vol 21 (1) ◽  
pp. 37-54 ◽  
Author(s):  
J. A. Makowsky ◽  
M. Ziegler
Keyword(s):  
Model Theory ◽  
Topological Model ◽  
Interior Operator ◽  
Consistency Properties

Some model theory for game logics

1979 ◽  
Vol 44 (2) ◽  
pp. 147-152
Author(s):  
Judy Green
Keyword(s):  
Model Theory ◽  
Existence Theorems ◽  
Semantic Interpretation ◽  
Rule Based ◽  
Game Logic ◽  
Important Method ◽  
Consistency Property ◽  
Consistency Properties ◽  
Model Existence

Consistency properties and their model existence theorems have provided an important method of constructing models for fragments of L∞ω. In [E] Ellentuck extended this construction to Suslin logic. One of his extensions, the Borel consistency property, has its extra rule based not on the semantic interpretation of the extra symbols but rather on a theorem of Sierpinski about the classical operation . In this paper we extend that consistency property to the game logic LG and use it to show how one can extend results about and its countable fragments to LG and certain of its countable fragments. The particular formation of LG which we use will allow in the game quantifier infinite alternation of countable conjunctions and disjunctions as well as infinite alternation of quantifiers. In this way LG can be viewed as an extension of Suslin logic.

scholarly journals A note on topological model theory

1974 ◽  
Vol 81 (2) ◽  
pp. 159-171 ◽  
Author(s):  
Abraham Robinson
Keyword(s):  
Model Theory ◽  
Topological Model

Topological Model Theory

1980 ◽  
Author(s):  
Jörg Flum ◽  
Martin Ziegler
Keyword(s):  
Model Theory ◽  
Topological Model

Systematization of finite many-valued logics through the method of tableaux

1987 ◽  
Vol 52 (2) ◽  
pp. 473-493 ◽  
Author(s):  
Walter A. Carnielli
Keyword(s):  
Model Theory ◽  
Proof Theory ◽  
Completeness Theorem ◽  
First Order ◽  
Formal Systems ◽  
Skolem Theorem ◽  
Consistency Properties ◽  
Model Existence ◽  
Model Existence Theorem ◽  
Theory And Model

AbstractThis paper presents a unified treatment of the propositional and first-order many-valued logics through the method of tableaux. It is shown that several important results on the proof theory and model theory of those logics can be obtained in a general way.We obtain, in this direction, abstract versions of the completeness theorem, model existence theorem (using a generalization of the classical analytic consistency properties), compactness theorem and Löwenheim-Skolem theorem.The paper is completely self-contained and includes examples of application to particular many-valued formal systems.

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