## Philosophy Lexicon of Arguments | |||

Set Theory: set theory is the system of rules and axioms, which regulates the formation of sets. The elements are exclusively numbers. Sets contain individual objects, that is, numbers as elements. Furthermore, sets contain sub-sets, that is, again sets of elements. The set of all sub-sets of a set is called the power set. Each set contains the empty set as a subset, but not as an element. The size of sets is called the cardinality. Sets containing the same elements are identical. See also comprehension, comprehension axiom, selection axiom, infinity axiom, couple set axiom, extensionality principle. | |||

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Books on Amazon |
HC I 183 Set Theory / Hughes / Cresswell: no predicate variables, only predicate constants (finite or infinite) - their use is determined by axioms - somewhere: set theory: only one predicate and infinitely many objects - the only predicate: "is an element of". |
Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 |

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Ed. Martin Schulz, access date 2017-05-28