Lindenbaum-type Logical Structures

TL;DR

This paper explores and characterizes various classes of logical structures, focusing on Tarski- and Lindenbaum-types, establishing their distinctions, and providing foundational theorems and representations within universal logic.

Contribution

It offers new characterization theorems for Tarski- and Lindenbaum-type structures and clarifies their relationships through examples and separation results.

Findings

Characterization theorems for Tarski- and Lindenbaum-types

Separation of five classes of logical structures

Representation theorems for Tarski-Lindenbaum structures

Abstract

In this paper, we study some classes of logical structures from the universal logic standpoint, viz., those of the Tarski- and the Lindenbaum-types. The characterization theorems for the Tarski- and two of the four different Lindenbaum-type logical structures have been proved as well. The separations between the five classes of logical structures, viz., the four Lindenbaum-types and the Tarski-type have been established via examples. Finally, we study the logical structures that are of both Tarski- and a Lindenbaum-type, show their separations, and end with characterization, adequacy, minimality, and representation theorems for one of the Tarski-Lindenbaum-type logical structures.