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May 2021 Definable Continuous Solutions of Linear Equations
Saronsad Sokantika, Athipat Thamrongthanyalak
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Notre Dame J. Formal Logic 62(2): 345-352 (May 2021). DOI: 10.1215/00294527-2021-0019

Abstract

In this paper, we study a generalization of a question, raised by C. Fefferman and J. Kollár, on the existence of solutions of linear functional equations. Suppose that R is a definably complete expansion of a real closed field (R;+,). Let f,g1,,gk:RnR be continuous functions that are definable in R. We prove that if there exist continuous functions y1,,yk:RnR such that f=g1y1++gkyk, then there exist continuous functions y1,,yk such that y1,,yk are definable in R and f=g1y1++gkyk.

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Saronsad Sokantika. Athipat Thamrongthanyalak. "Definable Continuous Solutions of Linear Equations." Notre Dame J. Formal Logic 62 (2) 345 - 352, May 2021. https://doi.org/10.1215/00294527-2021-0019

Information

Received: 21 June 2020; Accepted: 21 November 2020; Published: May 2021
First available in Project Euclid: 9 June 2021

Digital Object Identifier: 10.1215/00294527-2021-0019

Subjects:
Primary: 03C64
Secondary: 47H10, 54H25

Rights: Copyright © 2021 University of Notre Dame

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Vol.62 • No. 2 • May 2021
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