Intermediate Set TheoryWiley, 11 set 1996 - 244 pagine The authors cover first order logic and the main topics of set theory in a clear mathematical style with sensible philosophical discussion. The emphasis is on presenting the use of set theory in various areas of mathematics, with particular attention paid to introducing axiomatic set theory, showing how the axioms are needed in mathematical practice and how they arise. Other areas introduced include the axiom of choice, filters and ideals. Exercises are provided which are suitable for both beginning students and degree-level students. |
Sommario
Some of the history of the concept of sets | 1 |
1 | 7 |
Firstorder logic and its use in set theory | 13 |
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absolute abstraction terms antichain assume atomic formulas automorphism axiom of choice axiom of extensionality axiom of foundation Boolean algebra Boolean-valued bound Cantor chain choice function class variables cofinality collection construction continuum hypothesis countable cumulative type structure define definition delta-system denote dense domain equivalent exercise extend fact finite sets follows forcing formal formula sequences free variables give given Gödel's hence hereditarily symmetric hold ideal infinite initial ordinal isomorphic language lattice limit ordinal mathematics model of ZF natural numbers Note notion ordered pairs pair-set paradox partial ordering permutations poset power-set axiom proof proper class properties prove quantifiers rank rank(x real numbers recursion theorem relation relativized replacement axiom restrict result satisfy set theory Skolem functions subgroups subset axiom sum-set suppose symbols transfinite induction transitive truth lemma uncountable well-ordering Zorn's lemma