Journal of Symbolic Logic

On LP-models of arithmetic

J. B. Paris and A. Sirokofskich

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We answer some problems set by Priest in [11] and [12], in particular refuting Priest’s Conjecture that all LP-models of Th(ℕ) essentially arise via congruence relations on classical models of Th(ℕ). We also show that the analogue of Priest’s Conjecture for IΔ0 + Exp implies the existence of truth definitions for intervals [0,a] ⊂e M ⊨ IΔ0 + Exp in any cut [0,a] ⊂e K ⊆e M closed under successor and multiplication.

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J. Symbolic Logic, Volume 73, Issue 1 (2008), 212-226.

First available in Project Euclid: 16 April 2008

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Paris, J. B.; Sirokofskich, A. On LP -models of arithmetic. J. Symbolic Logic 73 (2008), no. 1, 212--226. doi:10.2178/jsl/1208358750.

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