The dissertation consists of an introductory chapter and eight published articles centered around the following topics: (1) calibration of the interpretability strength of weak first-order theories; (2) determination of the (un)decidability of fine-grained fragments of the intended models of the aforementioned theories; and (3) investigation of algebraic properties of the lattice of interpretability degrees of computably enumerable essentially undecidable theories.

1. 1. J. Murwanashyaka, A weak theory of building blocks. Mathematical Logic Quarterly, vol. 70 (2024), pp. 233–254. doi: 10.1002/malq.202300015

2. 2. J. Murwanashyaka, Hilbert’s tenth problem for term algebras with a substitution operator. Computability, vol. 13 (2024), nos. 3–4, pp. 433–457. doi: 10.3233/COM-230444

3. 3. J. Murwanashyaka, Weak essentially undecidable theories of concatenation, part II. Archive for Mathematical Logic, vol. 63 (2024), pp. 353–390. doi: 10.1007/s00153-023-00898-y

4. 4. J. Murwanashyaka, F. Pakhomov, and A. Visser, There are no minimal essentially undecidable theories. Journal of Logic and Computation, vol. 34 (2024), no. 6, pp. 1159–1171. doi: 10.1093/logcom/exad005

5. 5. J. Murwanashyaka, Weak essentially undecidable theories of concatenation. Archive for Mathematical Logic, vol. 61 (2022), nos. 7–8, pp. 939–976. doi: 10.1007/s00153-022-00820-y.

6. 6. J. Murwanashyaka, Weak sequential theories of finite full binary trees, Revolutions and Revelations in Computability (U. Berger, J. N. Y. Franklin, F. Manea, and A. Pauly, editors), CiE 2022, Lecture Notes in Computer Science, Vol. 13359, Springer International Publishing, 2022, pp. 208–219. doi: 10.1007/978-3-031-08740-0_18.

7. 7. L. Kristiansen and J. Murwanashyaka, First-order concatenation theory with bounded quantifiers. Archive for Mathematical Logic, vol. 60 (2021), nos. 1–2, pp. 77–104. doi: 10.1007/s00153-020-00735-6.

8. 8. L. Kristiansen and J. Murwanashyaka, On interpretability between some weak essentially undecidable theories, Beyond the Horizon of Computability (M. Anselmo, G. Della Vedova, F. Manea, and A. Pauly, editors), CiE 2020, Lecture Notes in Computer Science, Vol. 12098, Springer International Publishing, 2020, pp. 63–74. doi: 10.1007/978-3-030-51466-2_6.

Abstract prepared by Juvenal Murwanashyaka

E-mail: murwanashyaka@math.cas.cz

URL: http://hdl.handle.net/10852/104677

The crystal structures of two arylcyclohexylamine derivatives – methoxmetamine·HCl (2-(3-methoxyphenyl)-2-(methylamino)cyclohexan-1-one hydrochloride, MMXE·HCl) and methoxetamine·HCl (2-(ethylamino)-2-(3-methoxyphenyl)cyclohexan-1-one hydrochloride, MXE·HCl) – have been determined using laboratory X-ray powder diffraction data contained in the Powder Diffraction File™. MMXE·HCl and MXE·HCl exhibit anesthetic and sedative effects and have been illicitly used as recreational drugs due to their dissociative hallucinogenic and euphoriant effects. The structure determination of MMXE·HCl and MXE·HCl was carried out with DASH, and the Rietveld refinements were performed with TOPAS Academic in monoclinic unit cells. The parameters obtained for MMXE·HCl were a = 15.0429(5) Å, b = 14.0721(5) Å, c = 6.5716(2) Å, β = 90.9864(14)°, and V = 1,390.91(8) Å3, with Z = 4 and space group P21/n. The parameters obtained for MXE·HCl were a = 8.7772(5) Å, b = 9.9528(7) Å, c = 8.5841(6) Å, β = 100.276(3)°, and V = 737.86(8) Å3, with Z = 2 and space group P21. The structures were validated by dispersion-corrected DFT calculations. Hirshfeld surface analysis and fingerprint plots calculations are also reported.

Using calibrated radiocarbon dates, this study investigates climate signals recorded in fluvial sedimentary archives from southern Poland, eastern Netherlands, and eastern Germany. Summed probability density functions (PDFs) were constructed and analyzed in the context of INTIMATE stratigraphy. The results indicate that fluvial sedimentation and erosion processes were closely linked to climate fluctuations, particularly during GS/GI and GI/GS transitions. The analyses indicate multi-scale relationships between regional geomorphological processes and global climate trends during the period from 50 to 15 cal kBP. This study provides a reconstruction of Late Pleistocene fluvial activity and highlights the need for more precise radiocarbon dates to refine correlations between regional and global climate events.

We prove a common refinement of theorems of Bergfalk and of Casarosa and Lambie-Hanson, showing that under certain hypotheses, the higher derived limits of a certain inverse system of abelian groups $\mathbf {A}$ do not vanish. The refined theorem has a number of interesting corollaries, including the nonvanishing of the second derived limit of $\mathbf {A}$ in many of the common models of set theory of the reals and in the Mitchell model. In particular, we disprove a conjecture of Bergfalk, Hrušák, and Lambie-Hanson that higher derived limits of $\mathbf {A}$ vanish in the Miller model.

The topic of this thesis lies in the intersection between proof theory and algebraic logic. The main object of discussion, constructive reasoning, was introduced at the beginning of the twentieth century by Brouwer, who followed Kant’s explanation of human intuition of spacial forms and time points: these are constructed step by step in a finite process by certain rules, mimicking constructions with straightedge and compass and the construction of natural numbers, respectively.

The aim of the present thesis is to show how classical reasoning, which admits some forms of indirect reasoning, can be made more constructive. The central tool that we are using are induction principles, methods that capture infinite collections of objects by considering their process of generation instead of the whole class. We start by studying the interplay between certain structures that satisfy induction and the calculi for some non-classical logics. We then use inductive methods to prove a few conservation theorems, which contribute to answering the question of which parts of classical logic and mathematics can be made constructive.

Abstract prepared by Giulio Fellin

E-mail: giulio.fellin@univr.it

URL: https://researchportal.helsinki.fi/en/publications/constructivisation-through-induction-and-conservation

Capitalism is in trouble, or so we have been told. I argue that Adam Smith has a lot to teach us about the future of capitalism. I first examine recent discussions about the current challenges and criticisms against capitalism such as the productivity slowdown, waning competition, the role of globalization, rising inequality, and climate change. I emphasize that there are some global trends, but there are also important national and regional differences reflecting differences in institutions and policy. Not only natural-scientific technology, but also social-scientific technology—that is, governance, policy, and institutions—matter. Then, I explain what Smith can teach us. First, Adam Smith conceives a truly inclusive capitalism: he takes income distribution into account when he argues for the desirability of economic development. Second, inclusive capitalism requires broad formation and sharing of knowledge among people. Third, the expansion of exchange and trade has beneficial effects, but we should be aware of its distributional consequences. Fourth, institutions matter. Fifth, proper law and institutions—the “system of natural liberty”—are essential to a well-functioning market economy. However, the “system of natural liberty” is not automatically achieved. Policy and institutions are history-dependent; therefore, history matters.

Since 2014, transcatheter paravalvular leak closure with the Occlutech Paravalvular Leak Device has been successfully accomplished in adults with high technical success. We describe the first successful use of the Occlutech Paravalvular Leak Device in the left atrio-ventricular valve in the United States in a 5-year-old child with a history of previously repaired atrio-ventricular septal defect.

Wolff-Parkinson-White syndrome, characterised by accessory pathways, is rarely seen with dextrocardia. We present a case of situs inversus-dextrocardia with Wolff-Parkinson-White syndrome successfully treated via catheter ablation using 3D mapping (EnSite Precision®). Adjustments included reversed electrocardiogram (ECG) electrode placement, EnSite patch positioning, and fluoroscopic views. Coronary sinus access required counterclockwise manoeuvers. Mapping identified a left-sided accessory pathway, necessitating transseptal puncture with mirror-image adjustments. Ablation at the optimal site resulted in success. This case highlights the feasibility of catheter ablation in dextrocardia with tailored procedural modifications.

The aim of this research is to examine student motivation to participate in general music classes. The research involves students aged 10–14 from a general education primary school in Croatia (N = 186). The results indicate that these students were motivated to engage in general music classes; however, a nonlinear decline in motivation was evident as students progressed through the school years. Girls were more motivated to participate in general music classes compared to boys, and students involved in additional musical activities reported higher levels of motivation. Furthermore, listening to music influenced students’ perceptions of general music lessons and was associated with their motivation.