Weak Theories of Concatenation and Arithmetic

Decidable and Undecidable Fragments of First-Order Concatenation Theory

“…The material in Section 8 of the textbook Leary & Kristiansen [9] is also related to the research presented in this paper. So is a series of papers that starts with with Grzegorczyk [4] and includes Grzegorczyk & Zdanowski [5], Visser [16] and Horihata [7]. These papers deal with the essential undecidability 3 of various first-order theories of concatenation.…”

First-order concatenation theory with bounded quantifiers

“…A rather recent line of research in concatenation theory has focused on interpretablity between weak first-order theories and essential undecidability. Grzegorczyk [5], Grzegorczyk and Zdanowski [6], Svejdar [22], Visser [24], Horihata [11] and Higuchi and Horihata [10] belong to this line. Another recent line of research has focused on word equations and formal languages.…”

First-Order Concatenation Theory with Bounded Quantifiers

“…A rather recent line of research in concatenation theory has focused on interpretablity between weak first-order theories and essential undecidability. Grzegorczyk [5], Grzegorczyk & Zdanowski [6], Svejdar [22], Visser [24], Horihata [11] and Higuchi & Horihata [10] belong to this line. Another recent line of research has focused on word equations and formal languages.…”