Models of PA: Standard Systems without Minimal Ultrafilters

zbMath1424.03018arXiv0901.1499MaRDI QIDQ5379655

Saharon Shelah

Publication date: 13 June 2019

Abstract: We prove that bold N, the standard model of arithmetic, has an uncountable elementary extension N such that there is no ultrafilter on the Boolean Algebra of subsets of bold N represented in N which is minimal (i.e. as in Rudin-Keisler order for partitions represented in N).

Full work available at URL: https://arxiv.org/abs/0901.1499

zbMATH Keywords

forcingmodel theoryPeano arithmeticminimal ultrafilterset theoretic model theory

Mathematics Subject Classification ID

Models of arithmetic and set theory (03C62) Models with special properties (saturated, rigid, etc.) (03C50) Other aspects of forcing and Boolean-valued models (03E40) Set-theoretic model theory (03C55)

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Related Items (1)

Models of expansions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb N}$\end{document} with no end extensions

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