Logic seminar: Thursday, July 14. "Concatenation Theory: A New Framework for Formalist Foundations of Mathematics" (Zlatan Damnjanovic)

Четверг, 14 июля, ПОМИ. Начало в 14:00.

Докладчик: Zlatan Damnjanovic (University of Southern California, Dornsife).

Тема: Concatenation Theory: A New Framework for Formalist Foundations of Mathematics.

Abstract

We present and philosophically motivate a formal framework for reconstructing fundamental concepts of ordinary mathematics based on an elementary theory of concatenation. We show how ordinary arithmetical operations usually defined recursively can be recovered within a first-order theory that does not presuppose the legitimacy of definitions by primitive recursion, and how the familiar properties of these operations such as associativity, commutativity and distributivity, usually established by inductive reasoning, can be derived without taking induction principles for granted. As a by-product, we establish mutual interpretability of Robinson Arithmetic, Q, and Adjunctive Set Theory with Extensionality, AST+EXT.