Set Theory and the Continuum Hypothesis |
Contents
Universally Valid Statements | 8 |
The LöwenheimSkolem Theorem | 17 |
Examples of Formal Systems | 23 |
Copyright | |
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assume Axiom of Choice Axiom of Infinity Axiom of Regularity Axiom of Replacement axioms of ZF c₁ c₂ cardinality clearly complete sequence consider Consis ZF consistent constant symbols contain Continuum Hypothesis contradiction COROLLARY countable ordinals defined denote elements enumerate equations existence finite sets follows forces B(c forcing conditions formal system formula in ZF free variable give given Gödel hence implies Incompleteness Theorem initial segment integers intuitively isomorphic LEMMA limited statement Löwenheim-Skolem theorem mathematics ment model for ZF notion number theory one-one p.r. function Power Set Axiom precisely proof provable prove Q forces quantifiers range of f real numbers recursive functions relation symbols relativized Replacement Axiom result rules set of integers set theory standard model subset transfinite induction transitive set true uncountable unique valid statement well-ordered sets Z₁ α α