Einführung in die Mengenlehre

Deiser, Oliver

doi:10.1007/978-3-642-01445-1

Cited by 6 publications

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“…which also lends its quadratic form to its subspaces. Requiring the exclusive choice between (6) xor 7to be conserved by Lorentz transformations seems at first glance to enlarge the set of invariants of the causal automorphismen group of M. But this requirement is already a member of said set because, as has just been shown, the causality condition (2) actually states the formation of an ordered type, or respectively, an ordered set (A, R ⊂ A × A). Firstly, the constraint of events being put in sequence along the x 0 -axis by the standard order < determines the binary relation R:…”

Section: Causality and Order Typesmentioning

confidence: 99%

Well-order as a construction principle for physical theories

Schust¹

2019

Eur. Phys. J. C

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Physics has up to now missed to express in mathematical terms the fundamental idea of events of a path in time and space uniquely succeeding one another. An appropriate mathematical concept that reflects this idea is a wellordered set. In such a set every subset has a least element. Thus every element of a well-ordered set has as its definite successor the least element of the subset of all elements larger than itself. This is apparently contradictory to the densely ordered real number lines which conventionally constitute the coordinate axes in any representation of time and space and in which between any two numbers exists always another number. In this article it is shown how decomposing this disaccord in favour of well-ordered sets causes spacetime to be discontinuous.

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Section: Causality and Order Typesmentioning

confidence: 99%

Well-order as a construction principle for physical theories

Schust¹

2019

Eur. Phys. J. C

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“…It then took several decades until Zermelo's system was completed, formalized, and understood and widely accepted as a foundational theory for all of mathematics. (See, e.g., Ebbinghaus, 2007;Ferreirós, 1999;Kanamori, 1996Kanamori, , 2003Deiser, 2009) for the development of set theory and some of the initial conceptual difficulties; see, for example, Blass & Gurevich (2004) for an informal discussion of the foundational role of sets.…”

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confidence: 99%

An Axiomatic Theory of Well-Orderings

Deiser

2011

The Review of Symbolic Logic

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We introduce a new simple first-order framework for theories whose objects are well-orderings (lists). A system ALT (axiomatic list theory) is presented and shown to be equiconsistent with ZFC (Zermelo Fraenkel Set Theory with the Axiom of Choice). The theory sheds new light on the power set axiom and on Gödel’s axiom of constructibility. In list theory there are strong arguments favoring Gödel’s axiom, while a bare analogon of the set theoretic power set axiom looks artificial. In fact, there is a natural and attractive modification of ALT where every object is constructible and countable. In order to substantiate our foundational interest in lists, we also compare sets and lists from the perspective of finite objects, arguing that lists are, from a certain point of view, conceptually simpler than sets.

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Normativität in den Öffentlichkeitstheorien

Jünger

Donges

2013

Normativität in Der Kommunikationswissenschaft

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Einführung in die Mengenlehre

Cited by 6 publications

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Well-order as a construction principle for physical theories

Well-order as a construction principle for physical theories

An Axiomatic Theory of Well-Orderings

Normativität in den Öffentlichkeitstheorien

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