First Order Concatenation Theory vs First Order Number Theory

Explore the similarities and differences between first-order concatenation theory and first-order number theory in this 28-minute lecture from the Hausdorff Trimester Program: Types, Sets and Constructions. Delve into the fundamental structures of both theories, comparing their universes, function symbols, and interpretations. Examine how concatenation theory's standard structure operates on strings over an alphabet, while number theory's focuses on natural numbers. Investigate the extension of concatenation theory with a binary relation symbol and the introduction of bounded quantifiers, drawing parallels to those used in number theory. Gain insights into recent research published on fragments of first-order concatenation theory and its decidable and undecidable aspects. Enhance your understanding of these mathematical theories and their applications in computer science and logic.