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On computation in the limit by non-deterministic Turing machines
(Scientific Proceedings of Latvia State University, 1974)
What is Mathematics: Gödel's Theorem and Around (Edition 2015)
(2015-01-25)
Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2015.
What is Mathematics: Gödel's Theorem and Around (Edition 2013)
(2013-06-23)
Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2013. ATTENTION! New Edition 2015 available at https://dspace.lu.lv/dspace/handle/7/5306.
Truth Demystified
(2015-11-05)
For further development, see Karlis Podnieks in ResearchGate.
How could we recognize truth, if we only have models, means of model-building, and the history of their evolution? Where is the truth in the cloud of models – ...
Вокруг теоремы Геделя
(Latvia State University, 1981)
Проведен методологический анализ природы математики. Показано, что сущность математического метода состоит в исследовании застывших моделей. Обоснована несостоятельность утверждений об ограниченности аксиоматического метода. ...
The double-incompleteness theorem
(Stiinca, Kishinev, 1976)
Let T be a strong enough theory, and M - its metatheory, both are consistent. Then there is a closed arithmetical formula H that is undecidable in T, but one cannot prove in M neither that H is T-unprovable, nor that H is ...
The double-incompleteness theorem
(Latvia State University, 1975)
Let T be a theory, Q - a metatheory of T. Under certain conditions there exist T-undecidable sentences for which this undecidability cannot be proved in Q.
For English translation and proof, see K. Podnieks What is ...
Explanation and Understanding in a Model-Based Model of Cognition
(2017-11-20)
This article is an experiment. Consider a minimalist model of cognition (models, means of model-building and history of their evolution). In this model, explanation could be defined as a means allowing to advance: production ...
Towards a General Definition of Modeling
(2010-11-24)
What is a model? Surprisingly, in philosophical texts, this question is asked (sometimes), but almost never – answered. Instead of a general answer, usually, some classification of models is considered. The broadest possible ...