Set Theory and the Continuum Hypothesis |
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3 | 49 |
THE CONSISTENCY OF THE CONTINUUM HYPOTHESIS | 85 |
4 | 94 |
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A₁ 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 existence finite sets follows forcing conditions formal system formula in ZF free variable give given Gödel's hence implies Incompleteness Theorem initial segment integers intuitively isomorphic LEMMA limited statement Löwenheim-Skolem theorem M₂ mathematics model for ZF notion number theory 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 valid statement weakly forces well-ordered sets Z₁ Z₂ α α