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2015 Boolean-Valued Second-Order Logic
Daisuke Ikegami, Jouko Väänänen
Notre Dame J. Formal Logic 56(1): 167-190 (2015). DOI: 10.1215/00294527-2835065

Abstract

In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the range of the second-order variables. In our Boolean-valued second-order logic, the second-order variables range over all Boolean-valued subsets and relations on the domain. We show that under large cardinal assumptions Boolean-valued second-order logic is more robust than full second-order logic. Its validity is absolute under forcing, and its Hanf and Löwenheim numbers are smaller than those of full second-order logic.

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Daisuke Ikegami. Jouko Väänänen. "Boolean-Valued Second-Order Logic." Notre Dame J. Formal Logic 56 (1) 167 - 190, 2015. https://doi.org/10.1215/00294527-2835065

Information

Published: 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1372.03090
MathSciNet: MR3326594
Digital Object Identifier: 10.1215/00294527-2835065

Subjects:
Primary: 03-06
Secondary: 03C95 , 03E40 , 03E57

Keywords: $\Omega$-logic , Boolean validity , Boolean-valued second-order logic , full second-order logic

Rights: Copyright © 2015 University of Notre Dame

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Vol.56 • No. 1 • 2015
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