On Representations of Intended Structures in Foundational Theories

Journal of Philosophical Logic 51 (2):283-296 (2022)

Abstract

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power and meta-theoretic properties when comparing first-order and second-order logic.

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Neil Barton
Universität Konstanz

References found in this work

Undecidable Theories.Alfred Tarski - 1953 - Amsterdam: North-Holland Pub. Co..
Second-Order Logic and Foundations of Mathematics.Jouko Väänänen - 2001 - Bulletin of Symbolic Logic 7 (4):504-520.

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