Provability Logic and the Completeness Principle

In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that prove the schemes $A\to\triangle A$ and $\Box\triangle S\to\Box S$ for $S\in\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\Sigma_1$-provability logic of Heyting Arithmetic

История возникновения католической общины города Севастополя и строительство римско-католического костёла

Цель статьи – проследить этапы формирования римско-католической общины города Севастополя и историю строительства римско-католического костёла во имя Священномученника Климента Римского

Кіноніми Кіровоградщини: особливості вибору кличок та способи їх творення

Стаття присвячена вивченню особливостей української кінонімії. Основну увагу зосереджено на дослідженні процесу номінації та способів словотворення кличок собак. Окремо розглянуто офіційні назви тварин, які мають родослівну.Статья посвящена изучению особенностей украинской кинонимии. Основное внимание сосредоточено на изучении процесса номинации и способах словообразования кличек собак. Отдельно рассмотрены официальные названия собак, имеющих родословную.The article is devoted to the research of the peculiarities of Ukrainian cynonymy. Most attention is taid to the research of the process of nomination and to the ways of formation of dogs' names. Special consideration is given to the official names of the animals with genealogy

Dual-contrast computed tomography enables detection of equine posttraumatic osteoarthritis in vitro

To prevent the progression of posttraumatic osteoarthritis, assessment of cartilage composition is critical for effective treatment planning. Posttraumatic changes include proteoglycan (PG) loss and elevated water content. Quantitative dual-energy computed tomography (QDECT) provides a means to diagnose these changes. Here, we determine the potential of QDECT to evaluate tissue quality surrounding cartilage lesions in an equine model, hypothesizing that QDECT allows detection of posttraumatic degeneration by providing quantitative information on PG and water contents based on the partitions of cationic and nonionic agents in a contrast mixture. Posttraumatic osteoarthritic samples were obtained from a cartilage repair study in which full-thickness chondral defects were created surgically in both stifles of seven Shetland ponies. Control samples were collected from three nonoperated ponies. The experimental (n = 14) and control samples (n = 6) were immersed in the contrast agent mixture and the distributions of the agents were determined at various diffusion time points. As a reference, equilibrium moduli, dynamic moduli, and PG content were measured. Significant differences (p < 0.05) in partitions between the experimental and control samples were demonstrated with cationic contrast agent at 30 min, 60 min, and 20 h, and with non-ionic agent at 60 and 120 min. Significant Spearman's rank correlations were obtained at 20 and 24 h (rho = 0.482-0.693) between the partition of cationic contrast agent, cartilage biomechanical properties, and PG content. QDECT enables evaluation of posttraumatic changes surrounding a lesion and quantification of PG content, thus advancing the diagnostics of the extent and severity of cartilage injuries

Provability Logic and the Completeness Principle

In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that prove the schemes $A\to\triangle A$ and $\Box\triangle S\to\Box S$ for $S\in\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\Sigma_1$-provability logic of Heyting Arithmetic

Provability logic and the completeness principle

The logic iGLC is the intuitionistic version of Löb's Logic plus the completeness principle A→□A. In this paper, we prove an arithmetical completeness theorems for iGLC for theories equipped with two provability predicates □ and △ that prove the schemes A→△A and □△S→□S for S∈Σ 1 . We provide two salient instances of the theorem. In the first, □ is fast provability and △ is ordinary provability and, in the second, □ is ordinary provability and △ is slow provability. Using the second instance, we reprove a theorem previously obtained by Mohammad Ardeshir and Mojtaba Mojtahedi [1] determining the Σ 1 -provability logic of Heyting Arithmetic

Provability logic and the completeness principle

The logic iGLC is the intuitionistic version of Löb's Logic plus the completeness principle A→□A. In this paper, we prove an arithmetical completeness theorems for iGLC for theories equipped with two provability predicates □ and △ that prove the schemes A→△A and □△S→□S for S∈Σ 1 . We provide two salient instances of the theorem. In the first, □ is fast provability and △ is ordinary provability and, in the second, □ is ordinary provability and △ is slow provability. Using the second instance, we reprove a theorem previously obtained by Mohammad Ardeshir and Mojtaba Mojtahedi [1] determining the Σ 1 -provability logic of Heyting Arithmetic

Provability Logic and the Completeness Principle

In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that prove the schemes $A\to\triangle A$ and $\Box\triangle S\to\Box S$ for $S\in\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\Sigma_1$-provability logic of Heyting Arithmetic

Mogelijkheden van 3D-printen in de geneeskunde : 5 jaar later

5 years ago, we described the emergence of 3D printing in medicine. It was about 3D printing of anatomical structures, patient-specific drilling guides, cutting templates and implants and printing of living cells, growth factors and biomaterials ('bioprinting'). Surgeons are increasingly making use of 3D printing possibilities in preparation of surgeries on patients with complicated anatomies. Using tangible 3D models, it is easier for surgeons to prepare for surgeries and discussions with patients. They can also use 3D models as a tool to help with the training of young surgeons. Permanent titanium implants are increasingly being printed. Bioprinting is still in its infancy and there are no direct clinical applications yet. As we already predicted 5 years ago, many hurdles still have to be taken before broad clinical application of bioprinted products will become a reality

Mogelijkheden van 3D-printen in de geneeskunde : 5 jaar later

5 years ago, we described the emergence of 3D printing in medicine. It was about 3D printing of anatomical structures, patient-specific drilling guides, cutting templates and implants and printing of living cells, growth factors and biomaterials ('bioprinting'). Surgeons are increasingly making use of 3D printing possibilities in preparation of surgeries on patients with complicated anatomies. Using tangible 3D models, it is easier for surgeons to prepare for surgeries and discussions with patients. They can also use 3D models as a tool to help with the training of young surgeons. Permanent titanium implants are increasingly being printed. Bioprinting is still in its infancy and there are no direct clinical applications yet. As we already predicted 5 years ago, many hurdles still have to be taken before broad clinical application of bioprinted products will become a reality