Weak forms of the Regularity Principle in the presence of equation image

Mathematical Logic Quarterly 59 (1-2):84-100 (2013)
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Abstract

We study the strength of weak forms of the Regularity Principle in the presence of equation image relative to other subsystems of equation image. In particular, the Bounded Weak Regularity Principle is formulated, and it is shown that when applied to E1 formulas, this principle is equivalent over equation image to equation image.

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10.1002/malq.201100100

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Citations of this work

Algebraic combinatorics in bounded induction.Joaquín Borrego-Díaz - 2021 - Annals of Pure and Applied Logic 172 (2):102885.

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References found in this work

On parameter free induction schemas.R. Kaye, J. Paris & C. Dimitracopoulos - 1988 - Journal of Symbolic Logic 53 (4):1082-1097.
Bounded existential induction.George Wilmers - 1985 - Journal of Symbolic Logic 50 (1):72-90.
Diophantine Induction.Richard Kaye - 1990 - Annals of Pure and Applied Logic 46 (1):1-40.
Pell equations and exponentiation in fragments of arithmetic.Paola D'Aquino - 1996 - Annals of Pure and Applied Logic 77 (1):1-34.

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