A standard model of Peano arithmetic with no conservative elementary extension

DOI10.1016/J.APAL.2008.07.005zbMath1156.03035OpenAlexW2091858051MaRDI QIDQ998319

Ali Enayat

Publication date: 28 January 2009

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2008.07.005

zbMATH Keywords

Peano arithmeticconservative extensionsecond-order arithmeticproper forcingelementary end extensions

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Models of arithmetic and set theory (03C62) Second- and higher-order arithmetic and fragments (03F35) Interpolation, preservation, definability (03C40) Set-theoretic model theory (03C55)

Related Items (6)

Models of expansions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb N}$\end{document} with no end extensions ⋮ Proper and piecewise proper families of reals ⋮ Unifying the model theory of first-order and second-order arithmetic via \(\mathrm{WKL}_0^\ast\) ⋮ An improper arithmetically closed Borel subalgebra of \(\mathcal P(\omega)\) mod FIN ⋮ Models of PA: Standard Systems without Minimal Ultrafilters ⋮ Destructibility and axiomatizability of Kaufmann models

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