Search results for "completeness theorems"
showing 7 items of 7 documents
Introduction to Mathematical Logic, Edition 2021
2021
Textbook for students in mathematical logic. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux and resolution methods. Herbrand's theorem. Sections 1, 2, 3 represent an extended translation of the corresponding chapters of the book: V. Detlovs, Elements of Mathematical Logic, Riga, University of Latvia, 1964, 252 pp. (in Latvian).
Phenomenological-Semantic Investigations into Incompleteness
2000
When today the phenomenologist surveys the history of the philosophical comprehension of Godel’s theorems, he is confronted with the realization that the decisive publications come almost exclusively from the sphere of analytic philosophy.1 But does phenomenology in the spirit of Husserl not mean to keep in step with the epochal results of the special sciences by working on the phenomenological understanding of them? Phenomenological research of this kind means the same as development of phenomenological theory of science (Wissenschaftstheorie). In connection with the incompleteness theorems, the latter would be confronted with fundamental questions such as, “To what extent can mathematical…
Formālisms kā reālās matemātikas filozofija: 14 argumenti
2015
Referāts Latvijas Universitātes 73.zinātniskajā konferencē 2015.gada 13.februārī.
Logic, Computing and Biology
2015
Logic and Computing are appropriate formal languages for Biology, and we may well be surprised by the strong analogy between software and DNA, and between hardware and the protein machinery of the cell. This chapter examines to what extent any biological entity can be described by an algorithm and, therefore, whether the Turing machine and the halting problem concepts apply. Last of all, I introduce the concepts of recursion and algorithmic complexity, both from the field of computer science, which can help us understand and conceptualise biological complexity.
What is Mathematics: Gödel's Theorem and Around (Edition 2015)
2015
Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2015.
Realism, metamathematics, and the unpublished essays
1995
This initial chapter is divided into two sections. The first is devoted to a brief exposition of the intuitive essence and the philosophical motivation of Godel’s main metamathematical results, namely his completeness theorem for elementary logic (1930) and his incompleteness theorems for arithmetic (1931). Thereafter some discussion of the different ways to confront the relationship between those results and Godel’s philosophical realism in logic and mathematics is offered. Thus, mathematical realism will be successively regarded as (i) a philosophical consequence of those results; (ii) a heuristic principle which leads to them; (iii) a philosophical hypothesis which is “verified” by them.…
Inductive inference of recursive functions: Qualitative theory
2005
This survey contains both old and very recent results in non-quantitative aspects of inductive inference of total recursive functions. The survey is not complete. The paper was written to stress some of the main results in selected directions of research performed at the University of Latvia rather than to exhaust all of the obtained results. We concentrated on the more explored areas such as the inference of indices in non-Goedel computable numberings, the inference of minimal Goedel numbers, and the specifics of inference of minimal indices in Kolmogorov numberings.