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

Authors
Neil Barton
Universität Konstanz
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.
Keywords higher-order logic  representation  structure
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Reprint years 2021, 2022
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DOI 10.1007/s10992-021-09628-2
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References found in this work BETA

Undecidable Theories.Alfred Tarski - 1953 - Amsterdam: North-Holland Pub. Co..
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1949 - Journal of Symbolic Logic 14 (3):188-188.

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