## Notre Dame Journal of Formal Logic

### Non-Fregean Propositional Logic with Quantifiers

#### Abstract

We study the non-Fregean propositional logic with propositional quantifiers, denoted by $\mathsf{SCI}_{\mathsf{Q}}$. We prove that $\mathsf{SCI}_{\mathsf{Q}}$ does not have the finite model property and that it is undecidable. We also present examples of how to interpret in $\mathsf{SCI}_{\mathsf{Q}}$ various mathematical theories, such as the theory of groups, rings, and fields, and we characterize the spectra of $\mathsf{SCI}_{\mathsf{Q}}$-sentences. Finally, we present a translation of $\mathsf{SCI}_{\mathsf{Q}}$ into a classical two-sorted first-order logic, and we use the translation to prove some model-theoretic properties of $\mathsf{SCI}_{\mathsf{Q}}$.

#### Article information

Source
Notre Dame J. Formal Logic Volume 57, Number 2 (2016), 249-279.

Dates
Accepted: 7 November 2013
First available in Project Euclid: 9 February 2016

http://projecteuclid.org/euclid.ndjfl/1455030205

Digital Object Identifier
doi:10.1215/00294527-3470547

Mathematical Reviews number (MathSciNet)
MR3482746

Zentralblatt MATH identifier
06585187

#### Citation

Golińska-Pilarek, Joanna; Huuskonen, Taneli. Non-Fregean Propositional Logic with Quantifiers. Notre Dame J. Formal Logic 57 (2016), no. 2, 249--279. doi:10.1215/00294527-3470547. http://projecteuclid.org/euclid.ndjfl/1455030205.

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