7 research outputs found
Episodes in Model-Theoretic Xenology: Rationals as Positive Integers in R#
Meyer and Mortensen’s Alien Intruder Theorem includes the extraor- dinary observation that the rationals can be extended to a model of the relevant arithmetic R♯, thereby serving as integers themselves. Al- though the mysteriousness of this observation is acknowledged, little is done to explain why such rationals-as-integers exist or how they operate. In this paper, we show that Meyer and Mortensen’s models can be identified with a class of ultraproducts of finite models of R♯, providing insights into some of the more mysterious phenomena of the rational models
Episodes in Model-Theoretic Xenology: Rationals as Positive Integers in R#
Meyer and Mortensen’s Alien Intruder Theorem includes the extraor- dinary observation that the rationals can be extended to a model of the relevant arithmetic R♯, thereby serving as integers themselves. Al- though the mysteriousness of this observation is acknowledged, little is done to explain why such rationals-as-integers exist or how they operate. In this paper, we show that Meyer and Mortensen’s models can be identified with a class of ultraproducts of finite models of R♯, providing insights into some of the more mysterious phenomena of the rational models
On elimination of quantifiers in some non-classical mathematical theories
Elimination of quantifiers is shown to fail dramatically for a group of
well-known mathematical theories (classically enjoying the property) against a
wide range of relevant logical backgrounds. Furthermore, it is suggested that
only by moving to more extensional underlying logics can we get the property
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