The Cardinalities of Intervals of Equational Theories and Logics

Key Points

• The aim is to explore the cardinalities associated with different intervals of equational theories and logics.
• Analyzed various equational theories and their corresponding logical frameworks.
• Compared the cardinalities of different intervals within these theories.
• Applied mathematical structures to identify relationships between theories.
• Identified distinct patterns in cardinalities across various equational theories.
• Results suggest a hierarchy of intervals with respect to cardinalities.
• Findings contribute to understanding the foundational aspects of logic in mathematical theories.