Philosophy Lexicon of Arguments

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Infinity Axiom: The infinity axiom is an axiom of set theory, which ensures that there are infinite sets. It is formulated in e.g. such a way that a construction rule is specified for the occurrence of elements of a described set. If {x} is the successor of x, the continuation is formed by the union x U {x}. See also set theory, successor, unification, axioms.

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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

 
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Books on Amazon
Berka I 474
Existence/existence acceptance/Tarski: Problem: if we now eliminate the existential conditions in the axioms, so the corresponding allocation disappears - every expression will continue to correspond with a natural number, but not vice versa to any natural number an expression -> axiom of infinity.
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Berka I 519
Axiom of infinity/Tarski: with him, we renounce the postulate according to which only the right statements in each individual domain should be provable propositions of logic.


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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.

Tarsk I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983

Brk I
K. Berka/L. Kreiser
Logik Texte Berlin 1983


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Ed. Martin Schulz, access date 2017-11-19