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A classical reconstruction of Wright's first-order logic of strict finitism is presented. Strict finitism is a constructive standpoint of mathematics that is more restrictive than intuitionism. Wright sketched the semantics of said logic in Wright (Realism, Meaning and Truth, chap 4, 2nd edition in 1993. Blackwell Publishers, Oxford, Cambridge, pp.107-75, 1982), in his strict finitistic metatheory. Yamada (J Philos Log. https://doi.org/10.1007/s10992-022-09698-w, 2023) proposed, as its classical reconstruction, a propositional logic of strict finitism under an auxiliary condition that makes the logic correspond with intuitionistic propositional logic. In this paper, we extend the propositional logic to a first-order logic that does not assume the condition. We will provide a sound and complete pair of a Kripke-style semantics and a natural deduction system, and show that if the condition is imposed, then the logic exhibits natural extensions of Yamada (2023)'s results., Comment: The author's final manuscript in 47 pages. The published version is 54 pages long due to its format. This abstract is that of the published version

The nodal-line semimetals NaAlSi and NaAlGe have significantly different ground states despite having similar electronic structures: NaAlSi exhibits superconductivity below 7 K, while NaAlGe exhibits semiconductive electrical conductivity at low temperatures, indicating the formation of a pseudogap at approximately 100 K. The origin of the pseudogap in NaAlGe is unknown but may be associated with excitonic instability. We investigated hole-doping effects on the ground state in the solid solution Na(Al1-xZnx)Ge and discovered that the pseudogap is suppressed continuously with increasing Zn content, followed by the appearance of a superconducting dome with the highest transition temperature of 2.8 K. This superconductivity most likely results from excitonic fluctuations., Comment: 7 pages, 9 figures

Tantalum thin films sputtered on unheated silicon substrates are characterized with microwaves at around 10 GHz in a 10 mK environment. We show that the phase of tantalum with a body-centered cubic lattice ($\alpha$-Ta) can be grown selectively by depositing a niobium buffer layer prior to a tantalum film. The physical properties of the films, such as superconducting transition temperature and crystallinity, change markedly with the addition of the buffer layer. Coplanar waveguide resonators based on the composite film exhibit significantly enhanced internal quality factors compared with a film without the buffer layer. The internal quality factor approaches $2\times 10^7$ at a large-photon-number limit. While the quality factor decreases at the single-photon level owing to two-level system (TLS) loss, we have identified the primary cause of TLS loss to be the amorphous silicon layer at the film-substrate interface, which originates from the substrate cleaning before the film deposition rather than the film itself. The temperature dependence of the internal quality factors shows a marked rise below 200 mK, suggesting the presence of TLS-TLS interactions. The present low-loss tantalum films can be deposited without substrate heating and thus have various potential applications in superconducting quantum electronics., Comment: 7 pages, 4 figures + Supplementary Material (8 pages, 5 figures)

Crispin Wright in his 1982 paper argues for strict finitism, a constructive standpoint that is more restrictive than intuitionism. In its appendix, he proposes models of strict finitistic arithmetic. They are tree-like structures, formed in his strict finitistic metatheory, of equations between numerals on which concrete arithmetical sentences are evaluated. As a first step towards classical formalisation of strict finitism, we propose their counterparts in the classical metatheory with one additional assumption, and then extract the propositional part of `strict finitistic logic' from it and investigate. We will provide a sound and complete pair of a Kripke-style semantics and a sequent calculus, and compare with other logics. The logic lacks the law of excluded middle and Modus Ponens and is weaker than classical logic, but stronger than any proper intermediate logics in terms of theoremhood. In fact, all the other well-known classical theorems are found to be theorems. Finally, we will make an observation that models of this semantics can be seen as nodes of an intuitionistic model., Comment: 21 pages. Already published

NaAlSi and NaAlGe are isostructural and isoelectronic semimetals with topological nodal lines close to the Fermi level. Despite having virtually identical electronic structures, NaAlSi exhibits superconductivity below Tc = 6.8 K, whereas NaAlGe does not. We investigate NaAlGe by measuring its electrical resistivity, Hall effect, magnetic susceptibility, and heat capacity using single crystals. It is revealed that NaAlGe is not a simple semimetal but rather has an unusual ground state with a small pseudogap of approximately 100 K close to the Fermi level. We argue that the formation of the pseudogap in NaAlGe is due to an unexpected Fermi surface instability, such as an excitonic instability, as opposed to the electron-phonon instability that leads to the formation of the superconducting gap in NaAlSi., Comment: 6 pages, 5 figures

NaAlSi is a quasi-two-dimensional semimetal with superconductivity below Tc = 6.8 K and a band structure characterized by nodal lines near the Fermi level and potential topological surface states. Electrical resistivity measurements on its superconducting transitions in magnetic fields were made using plate-like single crystals. In the magnetic field-temperature phase diagram, we observed a substantial reduction in resistivity in a pre-transitional zone above the bulk superconducting regime only when the magnetic fields were perpendicular to the plane, rather than parallel to it. Significant sample (thickness) dependence, reentrant behavior, and sensitivity to electrode configurations all indicate that a portion of the crystal has an upper critical field greater than the bulk superconductivity in the pre-transitional region. This fractional superconductivity may occur on the side surface of the crystal.

Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be integrated on a computer. However, that method treats integration as equivalent to natural language translation and does not reflect mathematical information. In this study, we adjusted the learning model to take mathematical information into account and developed a wide range of learning models that learn the order of numerical operations more robustly. In this way, we achieved a 98.80% correct answer rate with symbolic integration, a higher rate than that of any existing method. We judged the correctness of the integration based on whether the derivative of the primitive function was consistent with the integrand. By building an integrated model based on this strategy, we achieved a 99.79% rate of correct answers with symbolic integration.

NaAlSi is an sp electron superconductor crystallizing in a layered structure of the anti-PbFCl type with a relatively high transition temperature Tc of ~7 K. Recent electronic state calculations revealed the presence of topological nodal lines in the semimetallic band structure, which attracted much attention owing to the superconductivity. However, experimental investigation remained limited because of the lack of single crystals. Here, we successfully prepared single crystals of NaAlSi by a Na-Ga flux method and characterized their superconducting and normal-state properties through electrical resistivity, magnetization, and heat capacity measurements. A sharp superconducting transition with a Tc of 6.8 K is clearly observed, and heat capacity data suggest an anisotropic superconducting gap. Surprisingly, despite the sp electron system, the normal state is governed by the electron correlations, which is indicated by a T2 resistivity and a Wilson ratio of 2.0. The origin of the electron correlation may be related to the orthogonal saddle-shaped Fermi surfaces derived from the Si px and py states, which intersect with the light Al s bands to form the nodal lines near the Fermi level. These results strongly suggest that the superconductivity of NaAlSi is not caused by a simple phonon mechanism but involves a certain unconventional aspect, although its relevance to the nodal lines is unclear.