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Jose Moncayo, Pedro H. Zambrano · 2023 · arXiv
We investigate different set-theoretic constructions in Residuated Logic based on Fitting's work on Intuitionistic Set Theory. We start by stating some results concerning constructible sets within valued models of Set Theory. We present two distinct constructions of the constructible universe: $\mathfrak{L}^{\mathbb{Q}}$ and $\mathbb{L}^{\mathbb{Q}}$, and show that they are isomorphic to V (the classical von Neumann universe) and L (the classical Gödel constructible universe), respectively. Even though lattice-valued models are the natural way to study non-classical Set Theory (e.g., Intuition
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Jan A. Bergstra, Inge Bethke · 2015 · arXiv
$\mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0$. In this note, we prove that $\mathbb{Q}_0$ cannot be specified by the usual axioms for meadows augmented by a finite set of axioms of the form $(1+ \cdots +1+x^2)\cdot (1+ \cdots +1 +x^2)^{-1}=1$.
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J. Silverio Martinez-Baena, Salvador Villegas · 2024 · arXiv
In the regularity theory of solutions to elliptic partial differential equations often the concept of stability plays the role of a sufficient condition for smoothness. It is a natural question to ask if this holds true for nonstable but finite Morse index solutions. We provide a negative answer showing the existence of sequences of solutions with radial Morse index equal to 1 for which regularity estimates can not be satisfied.
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Paweł Pasteczka · 2013 · arXiv
In the present paper we are going to prove some necessary condition for a mean to be Hardy. This condition is then applied to completely characterize the Hardy property among the Gini means.
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Grigor Sargsyan · 2021 · arXiv
We show that in extender models there are no generic embeddings with critical point $ω_1$ that resemble the stationary tower at the second Woodin cardinal.
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