scholarly journals The Prospects for Mathematical Logic in the Twenty-First Century

2001 ◽  
Vol 7 (2) ◽  
pp. 169-196 ◽  
Author(s):  
Samuel R. Buss ◽  
Alexander S. Kechris ◽  
Anand Pillay ◽  
Richard A. Shore
Keyword(s):  
Mathematical Logic ◽  
Computer Science ◽  
Set Theory ◽  
Model Theory ◽  
Proof Theory ◽  
Recursion Theory ◽  
First Century ◽  
Future Developments ◽  
The Future ◽  
Twenty First Century

AbstractThe four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.

One hundred and two problems in mathematical logic

1975 ◽  
Vol 40 (2) ◽  
pp. 113-129 ◽  
Author(s):  
Harvey Friedman
Keyword(s):  
Mathematical Logic ◽  
Set Theory ◽  
Model Theory ◽  
Proof Theory ◽  
Recursion Theory ◽  
Logic Model ◽  
Mathematical Statement ◽  
Question Mark ◽  
Truth Value ◽  
Expository Paper

This expository paper contains a list of 102 problems which, at the time of publication, are unsolved. These problems are distributed in four subdivisions of logic: model theory, proof theory and intuitionism, recursion theory, and set theory. They are written in the form of statements which we believe to be at least as likely as their negations. These should not be viewed as conjectures since, in some cases, we had no opinion as to which way the problem would go.In each case where we believe a problem did not originate with us, we made an effort to pinpoint a source. Often this was a difficult matter, based on subjective judgments. When we were unable to pinpoint a source, we left a question mark. No inference should be drawn concerning the beliefs of the originator of a problem as to which way it will go (lest the originator be us).The choice of these problems was based on five criteria. Firstly, we are only including problems which call for the truth value of a particular mathematical statement. A second criterion is the extent to which the concepts involved in the statements are concepts that are well known, well denned, and well understood, as well as having been extensively considered in the literature. A third criterion is the extent to which these problems have natural, simple and attractive formulations. A fourth criterion is the extent to which there is evidence that a real difficulty exists in finding a solution. Lastly and unavoidably, the extent to which these problems are connected with the author's research interests in mathematical logic.

Logic and Philosophical Methodology

2016 ◽  
Author(s):  
John P. Burgess
Keyword(s):  
Set Theory ◽  
Model Theory ◽  
Classical Logic ◽  
Proof Theory ◽  
Recursion Theory ◽  
Theory Model ◽  
Philosophical Methodology ◽  
Paraconsistent Logics ◽  
Philosophical Logic

This article explores the role of logic in philosophical methodology, as well as its application in philosophy. The discussion gives a roughly equal coverage to the seven branches of logic: elementary logic, set theory, model theory, recursion theory, proof theory, extraclassical logics, and anticlassical logics. Mathematical logic comprises set theory, model theory, recursion theory, and proof theory. Philosophical logic in the relevant sense is divided into the study of extensions of classical logic, such as modal or temporal or deontic or conditional logics, and the study of alternatives to classical logic, such as intuitionistic or quantum or partial or paraconsistent logics. The nonclassical consists of the extraclassical and the anticlassical, although the distinction is not clearcut.

Forcing in Proof Theory

2004 ◽  
Vol 10 (3) ◽  
pp. 305-333 ◽  
Author(s):  
Jeremy Avigad
Keyword(s):  
Mathematical Logic ◽  
Set Theory ◽  
Intuitionistic Logic ◽  
Model Theory ◽  
Proof Theory ◽  
Categorical Logic ◽  
Theory And Model ◽  
Number Of Branches

AbstractPaul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments.

Wilfrid Hodges A short history of model theory

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Mathematical Model ◽  
Number Theory ◽  
Set Theory ◽  
Model Theory ◽  
First Century ◽  
Historical Account ◽  
Short History ◽  
Early Twenty ◽  
History Of ◽  
Twenty First Century

We give a historical account of mathematical model theory, from its origins to the early twenty-first century. We record how early work in model theory grew from attempts to formalise and systematise some largely informal ideas in mathematical heuristics. We also note how the growth of model theory, particularly in recent years, has been driven by the discovery of interactions with many other areas of mathematics, such as set theory, combinatorics, algebra, geometry and number theory.

Pietro Basso,Modern Times, Ancient Hours: Working Livesin the Twenty-first Century. London: Verso, 2003. pp. 275. $27.00 cloth.

2005 ◽  
Vol 68 ◽  
pp. 134-136
Author(s):  
Gerd-Rainer Horn
Keyword(s):  
Everyday Life ◽  
Working Time ◽  
First Century ◽  
Recent Past ◽  
Social Scientists ◽  
Modern Times ◽  
The Future ◽  
Twenty First Century

For some time now, sociologists, economists and assorted futurologists have flooded the pages of learned journals and the shelves of libraries with analyses of the continuing decline of industrial and other forms of labor. In proportion to the decline of working time, those social scientists proclaim, the forward march of leisure has become an irresistible trend of the most recent past, the present and, most definitely, the future. Those of us living on planet earth have on occasion wondered about the veracity of such claims which, quite often, appear to stand in flat contradiction to our experiences in everyday life. The work of the Italian sociologist Pietro Basso is thus long overdue and proves to be a welcome refutation of this genre of, to paraphrase Basso, obfuscating hallucinations.

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