Article
A Note on Σ₁-Maximal Models
Author/s | Cordón Franco, Andrés
![]() ![]() ![]() ![]() ![]() ![]() ![]() Fernández Margarit, Alejandro Lara Martín, Francisco Félix ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial |
Publication Date | 2007 |
Deposit Date | 2021-04-09 |
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Abstract | Let T be a recursive theory in the language of first order Arithmetic. We prove that if T extends: (a) the scheme of parameter free Δ₁-minimization (plus exp), or (b) the scheme of parameter free Π₁-induction, then there ... Let T be a recursive theory in the language of first order Arithmetic. We prove that if T extends: (a) the scheme of parameter free Δ₁-minimization (plus exp), or (b) the scheme of parameter free Π₁-induction, then there are no Σ₁-maximal models with respect to T. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ₁-maximal models with respect to IΔ₀ + exp do not satisfy the scheme of Σ₁-collection BΣ₁. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España Junta de Andalucía |
Project ID. | MTM2005-08658
![]() TIC-137 ![]() |
Citation | Cordón Franco, A., Fernández Margarit, A. y Lara Martín, F.F. (2007). A Note on Σ₁-Maximal Models. The Journal of Symbolic Logic, 72 (3), 1072-1078. |
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