Lindenbaum-type Logical 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.
Keywords
Cite
@article{arxiv.2107.10768,
title = {Lindenbaum-type Logical Structures},
author = {Sayantan Roy and Sankha S. Basu and Mihir K. Chakraborty},
journal= {arXiv preprint arXiv:2107.10768},
year = {2022}
}
Comments
The final version of the article has been submitted to Logica Universalis. This version contains some major revisions and expansions