File Name: basic concepts of mathematics and logic .zip
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Some clarifications and mathematical definitions which are concerned with the many fundamental concepts of computability theory based directly on the computer field, are presented.
The sole aim of this paper is to attempt to bridge the gulf between the computer field on the one hand, and mathematics and logic on the other. The particular concepts are presented here for justification only: and therefore almost no theorems are included.
Fortunately there is no employer who could press me to prove the theorems! The intention is to provide such mathematical definitions as would be very relevant to computers and to their languages, and even more, to their development and design. Unable to display preview. Download preview PDF. Skip to main content. This service is more advanced with JavaScript available.
Advertisement Hide. Basic Concepts of Computer Science and Logic. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Tarski, A. Google Scholar. Carnap, R.
Russell, B. Wittgenstein, L. Wijngaarden, A. Centrum, Amsterdam, Bauer, F. McCarthy, J. Neumann, J. Mostowski, A. Krotsel, G. Shoenfield, J. Petri, C. Culik, K. Academy of Sciences, Prague, — Pawlak, Z. Manna, Z. Aho , Prentice Hall , pp. Engeler, E. Engeler , Springer Lecture Notes in Math. Hladky, M. Hajek, P. Engles, R. Codd, E. Kent, W. Luckham, D. Park, D. CrossRef Google Scholar. Personalised recommendations. Cite chapter How to cite?
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Abstract Set Theory by Thoralf A. Skolem, , PDF. Algebraic Logic by H. Andreka, I. Nemeti, I. Aschenbrenner, L. Axiomatic Set Theory I by A.
Set theory is a branch of mathematical logic that studies sets , which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used to define nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the s. After the discovery of paradoxes in naive set theory , such as Russell's paradox , numerous axiom systems were proposed in the early twentieth century, of which the Zermelo—Fraenkel axioms , with or without the axiom of choice , are the best-known.
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Set theory , branch of mathematics that deals with the properties of well-defined collections of objects, which may or may not be of a mathematical nature, such as numbers or functions. The theory is less valuable in direct application to ordinary experience than as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts. Between the years and , the German mathematician and logician Georg Cantor created a theory of abstract sets of entities and made it into a mathematical discipline.
Some clarifications and mathematical definitions which are concerned with the many fundamental concepts of computability theory based directly on the computer field, are presented. The sole aim of this paper is to attempt to bridge the gulf between the computer field on the one hand, and mathematics and logic on the other. The particular concepts are presented here for justification only: and therefore almost no theorems are included.
Mathematical logic , also called formal logic , is a subfield of mathematics exploring the formal applications of logic to mathematics. It bears close connections to metamathematics , the foundations of mathematics , and theoretical computer science. Mathematical logic is often divided into the fields of set theory , model theory , recursion theory , and proof theory.
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Set theory , branch of mathematics that deals with the properties of well-defined collections of objects, which may or may not be of a mathematical nature, such as numbers or functions. The theory is less valuable in direct application to ordinary experience than as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts. Between the years and , the German mathematician and logician Georg Cantor created a theory of abstract sets of entities and made it into a mathematical discipline. This theory grew out of his investigations of some concrete problems regarding certain types of infinite sets of real numbers. A set, wrote Cantor, is a collection of definite, distinguishable objects of perception or thought conceived as a whole. The objects are called elements or members of the set. The theory had the revolutionary aspect of treating infinite sets as mathematical objects that are on an equal footing with those that can be constructed in a finite number of steps.
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