H. Andréka, Á. Kurucz, I. Németi and I. Sain:
Applying Algebraic Logic; a General Methodology
Connections between Algebraic Logic and (ordinary) Logic. Algebraic
counterpart of model theoretic semantics, algebraic counterpart of proof
theory, and their connections. The class Alg(L) of
algebras associated to any logic L. Equivalence theorems stating
that L has a certain logical property iff Alg(L)
has a certain algebraic property. (E.g., L admits a strongly
complete Hilbertstyle inference system iff Alg(L)
is a finitely axiomatizable quasivariety. Similarly, L is compact iff
Alg(L) is closed under taking ultraproducts;
L has the Craig interpolation
property iff Alg(L) has the amalgamation property, etc.)
Contents

Introduction . . . . 2

General framework for studying logics . . . . 4

Defining the framework . . . . . 4
 Distinguished logics . . . . 11

Answers/solutions for important and hard exercises of
section 2.2 . . . . 32

Bridge between the world of logics and the world of algebras . . . . 34

Finetuning the framework . . . . 34

Algebraic characterizations of completeness and compactness
properties via Alg_m and Alg_= (main theorems) . . . . 40

Generalizations. . . . . 59

Appendix A: New kinds of logics . . . . 63

Appendix B: Further equivalence results . . . . 67

References . . . . 71
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