Modern Algebra and the Rise of Mathematical Structures

Corry, Leo

doi:10.1007/978-3-0348-7917-0

Cited by 233 publications

(97 citation statements)

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“…Then and only then a criterion of identity for the new, abstract entities can be extracted. In other words, the criterion of identity can not be given a priori but is derived from the theory 4 .…”

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confidence: 99%

Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics

Marquis

2016

Math Intelligencer

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In this paper, following the claims made by various mathematicians, I try to construct a theory of levels of abstraction. I first try to clarify the basic components of the abstract method as it developed in the first quarter of the 20th century. I then submit an explication of the notion of levels of abstraction. In the final section, I briefly explore some of main philosophical consequences of the theory.

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confidence: 99%

Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics

Marquis

2016

Math Intelligencer

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“…8 The first is general (or theoretic) model theory, while the second is subject-specific model theory. We may count under general model theory for first-order logic, such results as the Löwenheim-Skolem theorem (later extended in the "upward" direction by Tarski), the completeness theorem, the compactness theorem, the interpolation theorems, preservation theorems, the ultraproduct theorem, and so on.…”

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“…It has also been vigorously disputed publicly by Saul Kripke, though not in writing as far as I know. 8 Cf. also [31].…”

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On Rereading van Heijenoort’s Selected Essays

Feferman

2012

Log. Univers.

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Abstract. This is a critical reexamination of several pieces in van Heijenoort's Selected Essays that are directly or indirectly concerned with the philosophy of logic or the relation of logic to natural language. Among the topics discussed are absolutism and relativism in logic, mass terms, the idea of a rational dictionary, and sense and identity of sense in Frege. Mathematics Subject Classification. 03-03, 03A05.Keywords. Jean van Heijenoort, philosophy of logic, history of logic.

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“…Die anderthalb wissenschaftliche Generationen später -unabhän- (Purkert 1971(Purkert , 1972(Purkert , 1973 und zur Algebrentheorie (Schlote 1983(Schlote , 1986 Corry (1996) neu gesichtet.…”

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Scholz

2010

N.T.M.

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Modern Algebra and the Rise of Mathematical Structures

Cited by 233 publications

References 0 publications

Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics

Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics

On Rereading van Heijenoort’s Selected Essays

Die Explizierung des Impliziten

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